Distribution Of Tangential Stresses Research Articles

STRESSES IN ORTHOTROPIC CIRCULAR CYLINDRICAL SHELLS WITH LARGE-SIZE REINFORCED HOLES - A FOURIER SERIES APPROACH

An analytical solution for tangential stress distribution around large-size reinforced circular holes up to a shell curvature parameter of β = 2 in an orthotropic circular cylindrical shell under uniaxial load is derived. For this purpose, a new parameter a linearly proportional to β for an unreinforced large-size hole is determined using a finite element analysis and introduced in the existing Fourier series solution for small holes. For various hole sizes, optimum uniform thickness over the shell surface around the hole is assessed based on the unreinforced shell-to-plate stress ratio. For each hole size corresponding to each stress ratio, the reinforced shell solution converges to the case of unreinforced circular hole in an orthotropic infinite plate.

ALTERNATIVE STUDY OF A BEVEL PUNCH-ASSISTED ECAE SCHEME

It is a common practice in pressure forming to make an Equal Channel Angular Extrusion (ECAE) of a workpiece through a die with channel intersection angle 2θ = 90° using a standard punch of brick or cylindrical shape with 2θ0 = 90°. However Nejadseyfi et al (2015) have applied a beveled 2θ0-punch to the process of ECAE through a standard angular die of Segal geometry with 2θ = 90° and 2θ0 ≠ 2θ. The scope of the article is focused on an alternative numerical study of Nejadseyfi-ECAE-Scheme using techniques of Computational Fluid Dynamics (CFD). A finite-difference method was applied to the numerical solution of the boundary value problem for the Navier-Stokes equations in the form of a vorticity transfer equation. The complex of 2D plots for CFD-derived fields of flow lines and flow velocities and 3D plots for spatial distributions of flow velocities and tangential stresses were firstly derived for Nejadseyfi-ECAE-Scheme during viscous flow of polymer workpiece models through angular die with 2θ = 90° for the different punch inclination angles 30° ≤ 2θ0 ≤ 150°. It was found that Nejadseyfi-ECAE-Scheme provides enhancement of the rotary modes of intensive deformations during ECAE. Results provide visualization of velocity gradients and macroscopic rotation and the illustration of Nejadseyfi et al’s ideas from an alternative CFD-based viewpoint.

The analysis of deformation behavior of antifriction polymeric materials using the example of a spherical bearing

Simulation of the contact interaction of the spherical bearing elements through an antifriction polymeric layer of three materials is considered in the work. The deformation theory of elastoplasticity was chosen as a model describing the behavior of antifriction polymers based on the results of experiments. In the framework of the numerical study it was found that the deformation path in the space of the principal values of the strain deviator have a low degree of curvature at the contact deformation of the bearing, which confirms the choice of the theory of small elastoplastic strains. The relative analysis of the deformation behavior of antifriction polymeric materials as an interlayer of a spherical bearing is carried out in the work. It was found that the antifriction layer of the modified PTFE provides a more favorable distribution of contact parameters: disconnection of contact surfaces near the free edge of the interlayer is absent; the decrease in the efficiency of the part of the structure is observed by 10% of the contact surface; the distribution of contact pressure and contact tangential stress is more uniform and minimal in magnitude than in the other two materials under consideration.

Elastoplastic Analysis of Two-Layered Circular Lining Based on the Unified Strength Theory

Based on the Unified Strength Theory (UST), elastoplastic analysis of the two-layered circular lining is carried out. The stresses, displacements, and the elastic and plastic zones in both layers are discussed under different values of Young’s moduli of the inner and outer layers. The results reveal that, compared to the single-layered lining, the tangential stress distributions in the two-layered linings are more reasonable along the radial direction, which is beneficial to enhance the overall elastic and plastic ultimate bearing capacities. When considering the intermediate stress (i.e., the axial load), the elastic ultimate bearing capacity will be higher. However, the plastic ultimate bearing capacity remains unchanged. Moreover, a comparison between the Unified Strength Theory and Tresca Criterion is analyzed as well.

INVESTIGATION OF THE STRESSED STATE OF THE ROLLING PROCESS WITH USING HARMONIC FUNCTIONS

On the basis of the method of harmonic functions, a general mathematical model for the different loading of the deformation focus in the conditions of the plane problem of the theory of plasticity is developed. The problem is posed and solved in a closed form. It is assumed that the solution is of a universal nature, both from the point of view of finding a given class of functions, as well as methods of force action on the deformation center. Under the conditions of the proposed method, for the first time a solution of the applied problem connected with asymmetric loading was obtained. In this case, a complex solution for the entire deformation zone shows that the zones of different metal flow exert a significant influence on each other, which was not taken into account earlier when the deformation center was examined separately. From the point of view of boundary conditions, a region of acceptable solutions was determined under asymmetric loading conditions. Calculations showed that the proposed method can be used not only in solving problems of metal working with pressure with different external effects on the deformation center, in particular during rolling, but also for analyzing the stress state of the metal at each point of the deformation center under the conditions of new technical developments. There is a multifactor effect of different rolling conditions on the power parameters of the process. Values such as coefficient of friction, shape factor, angle of capture change the magnitude and distribution of normal and tangential stresses along the length of the deformation zone. It should be noted that the ratio of the parameters coefficient of friction - angle of capture is the determining factor of the entire rolling process. The process can lose stability, on the verge of slipping, at the same time the circuit of contact stresses changes dramatically, from convex it turns into a concave or partially concave-tuyu.It is determined that the model adequately reacts to changes in technological parameters of the forming process. The distribution of contact normal stresses is characterized by a significant unevenness in length for the thin and medium strips. For medium and high poles, there is a decrease in the effect of contact friction, a more uniform distribution of stress along the length of the arc of contact. It is shown that the stress state of a metal is determined by unified expressions for the entire focus of plastic flow.ssions for the entire focus of plastic flow.

The edge effects in layered beams

The article presents the resolving system of equations for solving the problem of the stress-strain state of multilayer beams. The system of resolving equations allows us to solve a wide range of problems, such as shear, bending, normal separation for any number of layers. In the proposed model the interaction between layers is accomplished by the contact layer. The contact layer is an anisotropic medium which can be considered as a "brush" of short elastic rods. The use of contact layer allows avoiding problems such as the endless shear stresses at the boundary of layers near the beam end. Another feature of the proposed model is the strict satisfaction of boundary conditions. Due to the complexity of resolving system of equations we consider a two-layer beam as an example. In this case it is possible to obtain an analytical solution and to produce its analysis. The edge effects arising in a two-layer beam are considered in detail. The article shows that the distribution of tangential stresses in the zone of the edge effect is a complex nonlinear function. At the moment the adhesive interaction is characterized by a single value – the average strength. This value is the ratio of the breaking load to the bonding area. Since the nature of stress distribution is a nonlinear function, the average strength is not true. The obtained solution makes it possible to establish a relationship between the average and true strength of the adhesive interaction, and to define the parameters of the contact layer based on experimental data. The influence of mechanical and geometric characteristics of the model on stress-strain state of the beam is analyzed.

Three-dimensional Stress Analysis Study on Multi-Bolted Joints of Composite Plates

Single-lap bolted joint is the widely applied technique in joining parts of aerospace and civil engineering structures, due to joint efficiencies where staggered arrangements are commonly adopted. This particular joint type exhibits secondary bending phenomenon due to eccentric loading path. Stress analysis enables the structure engineers to predict the failure path and maximum stress that may lead to catastrophic failures. Stress analysis study were carried out in multi-bolted woven fabric kenaf reinforced polymer (WKRP) joints with variation of lay-up types, hole configurations and plate thicknesses. 3-D FEA modelling implemented here explicitly incorporates out-of-plane deformation to provide better prediction upon crack initiation from maximum stress exhibited along the hole boundary. WKRP plates tested were failed in net-tension where the crack propagated normal to its applied stress. It was found that plate variation (i.e., lay-up types, hole configurations and plate thicknesses) correspondingly affect tangential stress distributions along its hole boundary. Current 3-D models used modulus properties from independent experimental work which regarded as smeared-out properties through their plate thickness. Staggered configurations demonstrated more evenly stress distribution to their adjacent bolts due to stress resistance diagonally and larger staggered plate width. Slightly contrast in lay-up types where larger tangential stress is exhibited in cross-ply due to more volume fraction of 0° fiber direction. Larger tangential stress in thicker plates associated to effective friction stress transfer to give higher failure load. Effects of secondary bending is more prominent in cross-ply and thinner plates, assumption of smeared-out properties is less good due to plate edge lifting, however, effect of secondary bending phenomenon in multi-bolted is lesser than single-bolted joints.

Solution of a Transverse Plane Bending Problem of a Laminated Cantilever Beam Under the Action of a Normal Uniform Load

The paper presents an exact direct solution of a transverse plane bending problem of a laminated cantilever beam of small width under the action of a uniformly distributed load under the absolutely hard contact between the layers. The solution has been constructed with the aid of linear elasticity theory equations: to take into account the heterogeneous structure of the laminated beam, piecewise constant functions of elastic characteristics, which have been described analytically by means of shifted Heaviside functions, have been introduced into the Hooke’s law relationships. During the solution of problem, the normal stresses were expressed from static equations in terms of an unknown function of tangential stress distribution over the cross-section height. The use of the obtained expressions in the Hooke’s law relationships and Cauchy equations for linear strains made it possible to establish relationships between displacements and tangential stresses. The Cauchy equation that remained for angle strains gave a defining integro-differential equation, from which differential equations for the unknown tangential stress function and for all unknown integration functions have been derived. The solution of the derived equations is possible for the entire packet of layers without considering an individual layer, the final relations for stresses, strains and displacements describing the stress-strain state of the entire packet of composite beam layers. The constructed solution satisfies the boundary conditions and the conditions of the absolutely hard contact of the layers and is exact if the load distribution corresponds to the determined stress distribution. Using this solution, we have carried out a theoretical study of the stress-strain state of a three-layer beam. The obtained relation allow one to predict the strength and stiffness of multilayer structural composite elements and to construct application solutions for other elastic bending problems of laminated beams.

A Springback Prediction Model for Warm Forming of Aluminum Alloy Sheets Using Tangential Stresses on a Cross-Section of Sheet

Warm U-draw bending tests were performed on a 5182 aluminum alloy under isothermal and non-isothermal conditions, and the amounts of springback under the corresponding conditions were measured. Finite element method analyses were then conducted to calculate the tangential stress distribution on the cross-section of the sheet during the warm forming process. It was found that the experimentally measured springback values were proportionally related to the differences in the amounts of tangential stresses at the top and bottom layers of the sheet section. A functional model that can account for the correlation between the amount of springback and the difference in tangential stresses at the top and bottom layers of the sheet section was derived based on an Euler beam and a nonlinear flow stress model with temperature and strain rate dependencies. The developed model, which can predict springback behavior using only results of forming analyses of warm formed aluminum alloy sheets, is anticipated to provide for advancements in the understanding of springback behavior at warm temperatures and improve the efficiency of design and analysis processes used to fabricate parts with complicated shapes by saving considerable time and costs for the analysis of springback.

К вопросу о реконструкции остаточных напряжений и деформаций пластины после дробеструйной обработки

Предметом исследования является математическое описание формы и напряженно-деформированного состояния стальной пластины, подвергнутой односторонней дробеструйной обработке, его экспериментальное подтверждение и применение результатов для верификации методов реконструкции полей остаточных напряжений и деформаций по экспериментальным данным. Подобная пластина используются на производстве в качестве калибровочного образца для определения времени пневмодробеструйной обработки, необходимого для формирования в поверхностном слое обрабатываемого изделия сжимающих тангенциальных остаточных напряжений заданной величины, а сам метод калибровки оказывается удобным и довольно широко распространенным для различных способов поверхностно упрочняющей обработки. Источником остаточных напряжений в данном случае является пограничный слой пластических деформаций, наводимый рассматриваемым технологическим процессом. Для постановки задачи задается структура поля тензора пластических деформаций. Форма и напряженно-деформированное состояние упругой пластины с пограничным слоем пластических деформаций были рассчитаны численно, в результате чего были выявлены качественные особенности данных полей, ослаблены граничные условия задачи и сформулированы гипотезы о структуре решения соответствующей пространственной задачи теории упругости, которое далее было найдено аналитически. Показано, что в рамках приближения плоского напряженного состояния в поперечных направлениях результат точно соответствует формуле Давиденкова - Биргера, связывающей зависимость тангенциальной компоненты остаточных напряжений от координаты по толщине пластины с функцией прогибов. Получена явная формула для зависимости остаточной (пластической) деформации от координаты по толщине. Проанализированы источники погрешностей полученных выражений и способы их коррекции. Проведен эксперимент по односторонней дробеструйной обработке калибровочной пластины, изготовленной из закаленной стали 65Г, для которой выполнено травление обработанной поверхности с измерением изменения стрелы прогиба (метод Н. Н. Давиденкова). С помощью полученных экспериментальных данных были численно реконструированы профили остаточных напряжений и деформаций с разумной точностью. Результат применим к широкому классу задач для упругих тел с упрочняющими покрытиями, а также имеет определенную методическую ценность для усовершенствования основ экспериментального исследования таких задач, позволяет формулировать и подтверждать экспериментом гипотезы о структуре решения, изучать связь рассматриваемых полей в предельных случаях, верифицировать применение различных способов учета остаточных напряжений и деформаций в численных расчетах. Найденное решение может быть использовано для верификации полей напряжений и перемещений при выборе различных вариантов предварительно напряженных или деформированных поверхностных оболочечных конечных элементов в рамках пакетов прикладных программ для расчета усталостной долговечности деталей машин с поверхностными упрочняющими покрытиями и также представляется опорным для исследования поверхностно упрочненных тел с криволинейной свободной границей, к которым сводится большинство практически важных задач.

Investigation and Computer Design of the Technological Modes of Continuous Rolling of Thin Brass Strips with Specified Accuracy

We developed a software system for the numerical analysis and design of the technological modes of continuous rolling of copper and brass strips, which enables us to investigate and design the conditions of deformation required to form specified transverse deviations of the thickness of rolled products. We refined the regularities of the influence of various lubricants and the models of distribution of tangential stresses along the contact arc (according to Coulomb and Zibel) on the pressure, rolling forces, and transverse profiles of the strips of L63 brass. We give recommendations concerning the technological mode and contouring of the rolls in a Tandem-1000 continuous three-stand rolling mill-1000 at the Kirov Nonferrous Metals Processing Plant with an aim to reduce transverse deviations of the thickness of thin strips of L63 brass.

Stress distribution in two-dimensional silos.

Simulations of a polydispersed two-dimensional silo were performed using molecular dynamics, with different numbers of grains reaching up to 64 000, verifying numerically the model derived by Janssen and also the main assumption that the walls carry part of the weight due to the static friction between grains with themselves and those with the silo's walls. We vary the friction coefficient, the radii dispersity, the silo width, and the size of grains. We find that the Janssen's model becomes less relevant as the the silo width increases since the behavior of the stresses becomes more hydrostatic. Likewise, we get the normal and tangential stress distribution on the walls evidencing the existence of points of maximum stress. We also obtained the stress matrix with which we observe zones of concentration of load, located always at a height around two thirds of the granular columns. Finally, we observe that the size of the grains affects the distribution of stresses, increasing the weight on the bottom and reducing the normal stress on the walls, as the grains are made smaller (for the same total mass of the granulate), giving again a more hydrostatic and therefore less Janssen-type behavior for the weight of the column.

Displacements, Strains, and Stresses Investigations in an Inhomogeneous Rotating Hollow Cylinder Made of Functionally Graded Materials under an Axisymmetric Radial Loading

In this paper, an analytical and numerical study of strain fields, stress fields and displacements in a rotating hollow cylinder, whose walls were completely made in Functionally Graded Materials (FGM), was conducted. We have considered the rotating hollow cylinder submitted to an asymmetric radial loading. It is assumed that, because of the functional graduation of the material, the mechanical properties such as Young elastic modulus and the density varies in the radial direction, in accordance with a the power law function. The inhomogeneity parameter was selected between -1 and 1. On the basis of the second law of Newton, Hooke’s law and the strain-stress relationship, we established the differential equation which governs the equilibrium for a rotating hollow cylinder. We found the analytical solution and compared to the numerical solution obtained by using the shooting method and the fourth order Runge-Kutta algorithm. The analytical and numerical results lead to the conclusion that the magnitude of the tangential stresses is greater than that of the radial stresses. The changes due to the graduation of FGM does not produce consistent variations in the distribution of radial stresses, but strongly affects the distribution of tangential stresses. The tangential stresses, tangential strains and displacements are much higher at the inner surface of the cylinder wall. The internal radial pressure intensely affects the radial stresses and the radial strain.

MODELING OF STRESS-STRAIN STATE OF THICK CONCRETE SLABS TAKING THE CREEP OF CONCRETE INTO ACCOUNT

In the article the derivation of the resolving equations for calculation taking into account creep of thick reinforced concrete plates is given. We use the hypothesis of a parabolic law for the distribution of tangential stresses over the thickness of a plate. The problem was reduced to a system of two differential equations with respect to deflection and the function of shear. An example is given of a calculation of a plate hinged on the contour loaded with a uniformly distributed load using a viscoelastic model of hereditary aging of concrete. The solution was carried out using double trigonometric series in combination with the Euler method for determining creep strains.

Plane Thermoelastic Deformation of a Multilayer Plate Elastically Coupled with a Rigid Half Plane

We propose a method for the solution of two-dimensional stationary problems of thermoelasticity for a multilayer plate with elastic links between the layers elastically coupled with a rigid half plane. The procedure is based on the method of compliance functions with the use of the one-dimensional Fourier integral transformation. We construct the recurrence relations for the compliance functions that take into account the influence of thermal loads and the elastic links between layers. For a two-layer plate subjected to the action of thermal loads applied to the upper boundary of the plate, we analyze the influence of the elastic links, the coefficients of thermal expansion, and the heat-conduction coefficients on the distributions of normal and tangential stresses on the common boundary of the layers.

Closed Semiinfinite Crack on the Boundary of an Elastic Strip and a Rigid Wall

We analyze the compression and shear of an elastic strip weakened by a semiinfinite crack on the boundary of this strip and a rigid wall. The crack is completely closed, and its faces are under the conditions of friction sliding. By the Wiener–Hopf method, we obtain an analytic solution of the problem. The distributions of normal and tangential stresses on the crack line and on its continuation are determined. The stress intensity factor in shear is also obtained.

Fracture analysis of marble specimens with a hole under uniaxial compression by digital image correlation

To investigate the effects of pre-fabricated holes with different geometries, including size, shape and inclination angle, on the strength and fracture behavior of rock materials, a series of uniaxial compressive tests were conducted on prismatic marble specimens containing a circular or an elliptical hole using a servo-hydraulic machine synchronized with a charge-coupled device (CCD) camera. Digital image correlation (DIC) was applied to record and analyze the deformation and fracturing process of marble. Experimental results combined with theoretical analysis indicate that the geometries of the internal hole are important factors affecting the strength of marble and also the boundary tangential stress distribution. The specimen with a higher tangential compressive stress concentration coefficient will have a lower UCS values. Observations show that the evolution of deformation and fracturing process of marble specimens can be visually displayed by the apparent displacement and strain fields. The propagation of cracks is a progressive development of high major principal strain zones, and the process of damage accumulation, crack initiation and propagation of rock at different stress stages can be well reflected by DIC. When the stress increases to 78.2% of peak value, critical cracks initiate in the tensile stress concentration zones. The progressive process of “open-close-reopen” of tensile cracks was quantitatively studied by the tensile strain of the specimens. It was found that the propagation of tensile cracks surrounding the hole in marble specimens was mainly affected by the nucleation and propagation of strain localization zones.

CONTINUOUS CASTING AND DEFORMATION INSTALLATION FOR THE PRODUCTION OF STEEL PLATES FOR WELDED PIPES. REPORT 2

Technological feasibility of combined process and installation of continuous casting and deformation to obtain high mechanical properties and fine-grained structure of steel sheets for weld pipes are considered. The problem of metal stress-strain state under solidified metal cobbing by the die walls of assembly mold is stated taking into account a force of the liquid phase pulling from the permanent crystallizer of installation. Parameters of cyclic deformation focus for thin slab sheets production, initial data for design and boundary conditions of the problem are given. A design scheme for determining stress-strain state of metal in circular deformation focusis presented. Results are obtained by solving the problem of continuum mechanics by finite element method: flat statement of contact problem of elastic-plasticity was used in conditions of large deformations and displacements.ANSYS software was used to solve the problem. The calculation results are presented in form of stress diagrams along the strip symmetry axis and on part of contact line of deformation focus with the die wall. Regularities of distribution of tangential stresses on contact surface of circular deformation focus are presented. Evaluation of solidified metal flow on the boundary with liquid phase during solidified metal cobbing by die walls is provided taking into account a force of liquid phase pulling from permanent crystallizer. The estimation of stress state scheme of metal in circular deformation focus during thin slab cobbing with a high degree of deformation is described in order to improve quality of steel sheets for weld pipes production. The main parameters of continuous casting and deformation plant for weld pipes steel sheets production are given.

Численное исследование напряженно-деформированного состояния в окрестности горной выработки

A stress-strain state in the vicinity of excavation of the circular cross-section is studied in the paper. Formulas derived from the elasticity theory can be applied to the homogeneous rock formations of sufficient strength. The problem of determination of the displacement and stress fields is considered in the rectangular region with the circular hole. A numerical solution algorithm based on the finite element method is elaborated. The algorithm of constructing of a finite element mesh allows to take into account the shape, size and hole location. Fields of the displacements and stress are determined. Results of numerical calculations for holes of different diameters are presented. The influence of a hole size on the stress distribution in the vicinity of holes is presented. Isolines of the maximal tangential stress are constructed. The maximal tangential stress distribution is used to estimate the possibility of brittle fracture in the test region. Numerical modeling based on the constructed algorithm allows one to investigate the stress-strain state in the vicinity of excavation and to predict the possible plastic behavior and development of a material failure.

Modeling of bending characteristics of symmetric tri-layer laminated Sheet materials

Bending of sheet materials is widely applied to shaping many automotive, aerospace and other industrial components. Tailored laminate sheet materials are desirable in bending applications where monolithic sheets do not meet the design requirements or manufacturing demands. An accurate analytical model can be effectively utilized for rapid design of components for laminated sheet materials for a given application. Many analytical models based on advanced theory of bending have been proposed in the literature to predict plane strain bending characteristics of monolithic sheet materials. However, there are very few such models for laminated sheet materials. In this study, an analytical model for tri-layer laminated sheet material is developed based on advanced theory of bending. The model considers Mises yielding and Ludwik non-linear plastic hardening with Bauschinger effect for various laminate thickness ratios. Also, a 3D FE model based on Marciniak-Kuczynski (MK) bend test design is developed to assess pure bending characteristics of a symmetric tri-layer aluminum sheet laminate with softer and thinner clad layers on both surfaces and a harder thicker core in the middle. The through-thickness tangential stresses from the analytical model are compared with those from FE model for different clad to matrix thickness ratios. The tangential stresses decrease in magnitude with increasing aluminum clad thickness ratios in the analytical model. This behavior is in good general agreement with the results from the mid-width section for the FE model. The analytical and FE models also yield similar order trend in relative thickness change with increasing clad thickness ratios and with increasing specimen radius of curvature. The 3D FE model exhibited anticlastic curvature at the edges as a result of strain inhomogeneity across the width. Unlike the tangential stress distribution, the tangential strain is maximum at the specimen edges than at the mid-width. The inhomogeneity in stress and strain across the bend line shows that plane strain condition is not consistent across the width of the sheet.