scholarly journals Determination of the stress state of a hardening disk under the influence of temperature

2020 ◽  
pp. 168-173
Author(s):  
Мария Михайловна Вислогузова ◽  
Дмитрий Викторович Гоцев ◽  
Алексей Викторович Ковалев ◽  
Александр Иванович Шашкин
Keyword(s):  
Displacement Vector ◽  
Analytical Form ◽  
Radial Component ◽  
Inelastic Behavior ◽  
Small Perturbations ◽  
Flat Disk ◽  
Elastoplastic Boundary ◽  
Distribution Of Stress ◽  
Elastic And Plastic Deformation

Как известно при нагревании твердые тела, в частности металлы, испытывают температурные деформации, связанные с эффектом линейного расширения. При этом, несмотря на то, что эти деформации малы, соответствующие им напряжения могут оказаться достаточно большими, зачастую превосходящими предел текучести материала. В связи с этим для описания напряженно-деформированных состояний тел, находящихся под действием высоких температур, необходимо учитывать неупругое поведение материалов. Определению напряжений и деформаций в упругопластических задачах посвящено множество работ, в том числе исследования [1-10]. В некоторых из них [1], [5-10] рассматривается температурное воздействие на тела различной конфигурации. В настоящей работе решается задача об определении осесимметричного поля напряжений в плоском диске при воздействии на него точечного источника тепла (например, точечная сварка). Материал диска моделируется упрочняющейся упругопластической средой. Задача решалась в рамках плоско-напряженного состояния методом малых возмущений. В аналитическом виде получены соотношения, описывающие распределение полей напряжений в упругой и пластической областях деформирования. В качестве условий сопряжения решений на упругопластической границе использовались условия неразрывности радиальной и окружной компонент тензора напряжений и радиальной компоненты вектора перемещений. As you know, when heated, solids, in particular metals, experience thermal deformations associated with the effect of linear expansion. Moreover, in spite of the fact that these strains are small, the corresponding stresses can be quite large, often exceeding the yield stress of the material. In this regard, to describe the stress-strain states of bodies exposed to high temperatures, it is necessary to take into account the inelastic behavior of materials. Determination of stresses and strains in elastoplastic problems has been the subject of many works, including studies [1-10]. Some of them [1], [5-10] consider the temperature effect on bodies of various configurations. In this work, we solve the problem of determining the axisymmetric stress field in a flat disk when exposed to a point heat source (for example, spot welding). The disc material is modeled by a hardening elastoplastic medium. The problem was solved within the plane-stressed state by the method of small perturbations. In an analytical form, relations are obtained that describe the distribution of stress fields in elastic and plastic deformation regions. The conditions of continuity of the radial and circumferential components of the stress tensor and the radial component of the displacement vector were used as conditions for conjugation of solutions on the elastoplastic boundary.

scholarly journals On the determination of the voltage field in the eccentric tube, from an aging elasticplastic material

2020 ◽  
pp. 93-100
Author(s):  
Дмитрий Викторович Гоцев ◽  
Алексей Викторович Ковалев ◽  
Александр Иванович Шашкин ◽  
Александр Юрьевич Яковлев
Keyword(s):  
Analytical Form ◽  
Pipe Material ◽  
Elastoplastic Properties ◽  
Stress Components ◽  
History Of ◽  
Eccentric Tube ◽  
Distribution Of Stress ◽  
Analytical Expressions ◽  
Elastoplastic Stress State

В работе в ананлитическом виде определяется распределение полей напряжений в эксцентрической трубе, находящейся под действием внутреннего давления. Материал трубы моделировался средой, обладающей наследственно стареющими упругопластическими свойствами. Решение задачи проводилось в рамках метода возмущений. За малый параметр бралась величина эксцентриситета. В качестве невозмущенного состояния принималось осесимметричное упругопластическое напряженное состояние трубы, определенное с учетом возраста и истории нагружения материала. В результате моделирования выведено уравнение для определения формы и размера границы раздела упругой и пластичесой зон в трубе с эксцентриситетом, а также получены аналитические выражения для компонент напряжений в каждой из областей деформирования. In this work, the distribution of stress fields in an eccentric pipe under the action of internal pressure is determined in an analytical form. The pipe material was modeled by a medium with hereditarily aging elastoplastic properties. The problem was solved within the framework of the perturbation method. The eccentricity value was taken as a small parameter. The unperturbed state was taken to be the axisymmetric elastoplastic stress state of the pipe, determined taking into account the age and loading history of the material. As a result of modeling, an equation was derived to determine the shape and size of the interface between the elastic and plastic zones in a pipe with eccentricity, and analytical expressions were obtained for the stress components in each of the deformation regions.

The deformation of the ground around surface faults

1961 ◽  
Vol 51 (3) ◽  
pp. 355-372 ◽  
Author(s):  
M. A. Chinnery
Keyword(s):  
San Andreas Fault ◽  
Displacement Vector ◽  
Good Description ◽  
Analytical Form ◽  
Infinite Length ◽  
Dislocation Theory ◽  
Contour Maps ◽  
San Andreas ◽  
Limiting Case

Abstract A rectangular dislocation surface (i.e., a surface across which there is a discontinuity in the displacement vector) is used as a model of a vertical transcurrent fault. The results of Steketee (1958a) are employed to derive, in analytical form, the displacement field throughout a semi-infinite elastic medium due to such a dislocation. In particular, the displacements of the surface of the medium are calculated in some detail, and contour maps of the various components are given for two representative cases. The solution to the limiting case of a fault of infinite length is also included. Methods are then discussed for the determination of the depth of a surface fault from measurements of the deformation of the ground produced by it, and these are applied to the faults associated with the Tango and North Idu earthquakes, and to the San Andreas fault. In each of these cases, the general features of the crustal deformations agree well with the predictions of the theory, and it is concluded that dislocation theory provides a good description of the effects of fracture in the earth's crust.

Simulation and Contrast Analysis of tem Images of Cracks

1990 ◽  
Vol 48 (1) ◽  
pp. 578-579
Author(s):  
D. Goyal ◽  
A. H. King
Keyword(s):  
Displacement Vector ◽  
Crack Tip ◽  
Perfect Crystal ◽  
Operating Conditions ◽  
Displacement Fields ◽  
Fringe Contrast ◽  
Orthogonal Geometry ◽  
Moire Fringe ◽  
Moiré Fringe

TEM images of cracks have been found to give rise to a moiré fringe type of contrast. It is apparent that the moire fringe contrast is observed because of the presence of a fault in a perfect crystal, and is characteristic of the fault geometry and the diffracting conditions in the TEM. Various studies have reported that the moire fringe contrast observed due to the presence of a crack in an otherwise perfect crystal is distinctive of the mode of crack. This paper describes a technique to study the geometry and mode of the cracks by comparing the images they produce in the TEM because of the effect that their displacement fields have on the diffraction of electrons by the crystal (containing a crack) with the corresponding theoretical images. In order to formulate a means of matching experimental images with theoretical ones, displacement fields of dislocations present (if any) in the vicinity of the crack are not considered, only the effect of the displacement field of the crack is considered.The theoretical images are obtained using a computer program based on the two beam approximation of the dynamical theory of diffraction contrast for an imperfect crystal. The procedures for the determination of the various parameters involved in these computations have been well documented. There are three basic modes of crack. Preliminary studies were carried out considering the simplest form of crack geometries, i. e., mode I, II, III and the mixed modes, with orthogonal crack geometries. It was found that the contrast obtained from each mode is very distinct. The effect of variation of operating conditions such as diffracting vector (), the deviation parameter (ω), the electron beam direction () and the displacement vector were studied. It has been found that any small change in the above parameters can result in a drastic change in the contrast. The most important parameter for the matching of the theoretical and the experimental images was found to be the determination of the geometry of the crack under consideration. In order to be able to simulate the crack image shown in Figure 1, the crack geometry was modified from a orthogonal geometry to one with a crack tip inclined to the original crack front. The variation in the crack tip direction resulted in the variation of the displacement vector also. Figure 1 is a cross-sectional micrograph of a silicon wafer with a chromium film on top, showing a crack in the silicon.

scholarly journals The experimental determination of the diameter of a flat disk in a ridge seeder

2020 ◽  
Vol 971 ◽  
pp. 052055
Author(s):  
Evgeny Zykin ◽  
Vladimir Kurdyumov ◽  
Svetlana Lazutkina ◽  
Sergey Albutov
Keyword(s):  
Experimental Determination ◽  
Flat Disk

scholarly journals Crack Propagation Velocity Determination by High-speed Camera Image Sequence Processing

2020 ◽  
Author(s):  
Frank Liebold ◽  
Ali A. Heravi ◽  
Oliver Mosig ◽  
Manfred Curbach ◽  
Viktor Mechtcherine ◽  
...  
Keyword(s):  
Crack Propagation ◽  
High Speed ◽  
Vector Fields ◽  
Displacement Vector ◽  
Image Sequence ◽  
High Speed Camera ◽  
Sequence Processing ◽  
Image Sequence Processing ◽  
Propagation Velocities

The determination of crack propagation velocities can provide valuable information for a better understanding of damage processes of concrete. The spatio-temporal analysis of crack patterns developing at a speed of several hundred meters per second is a rather challenging task. In the paper, a photogrammetric procedure for the determination of crack propagation velocities in concrete specimens using high-speed camera image sequences is presented. A cascaded image sequence processing which starts with the computation of displacement vector fields for a dense pattern of points on the specimen’s surface between consecutive time steps of the image sequence chain has been developed. These surface points are triangulated into a mesh, and as representations of cracks, discontinuities in the displacement vector fields are found by a deformation analysis applied to all triangles of the mesh. Connected components of the deformed triangles are computed using region-growing techniques. Then, the crack tips are determined using principal component analysis. The tips are tracked in the image sequence and the velocities between the time stamps of the images are derived. A major advantage of this method as compared to established techniques is in the fact of its allowing for spatio-temporally resolved, full-field measurements rather than point-wise measurements and that information on crack width can be obtained simultaneously. To validate the experimentation, the authors processed image sequences of tests on four compact-tension specimens performed on a split-Hopkinson tension bar. The images were taken by a high-speed camera at a frame rate of 160,000 images per second. By applying to these datasets the image sequence processing procedure as developed, crack propagation velocities of about 800 m/s were determined with a precision in the order of 50 m/s.

scholarly journals Determination of the number of radicals in the initial chain reactions by mathematical methods

2009 ◽  
Vol 63 (2) ◽  
pp. 121-127
Author(s):  
Branko Pejovic ◽  
Milovan Jotanovic ◽  
Vladan Micic ◽  
Milorad Tomic ◽  
Goran Tadic
Keyword(s):  
General Chemistry ◽  
Difference Equation ◽  
Analytical Form ◽  
Mathematical Methods ◽  
Linear Difference Equations ◽  
Efficient Procedure ◽  
Chain Reactions ◽  
Chemical Equation ◽  
The Difference

Starting from the fact that the real mechanism in a chemical equation takes places through a certain number of radicals which participate in simultaneous reactions and initiate chain reactions according to a particular pattern, the aim of this study is to determine their number in the first couple of steps of the reaction. Based on this, the numbers of radicals were determined in the general case, in the form of linear difference equations, which, by certain mathematical transformations, were reduced to one equation that satisfies a particular numeric series, entirely defined if its first members are known. The equation obtained was solved by a common method developed in the theory of numeric series, in which its solutions represent the number of radicals in an arbitrary step of the reaction observed, in the analytical form. In the final part of the study, the method was tested and verified using two characteristic examples from general chemistry. The study also gives a suggestion of a more efficient procedure by reducing the difference equation to a lower order.

scholarly journals Determination of Lateral Modulation Apodization Functions Using a Regularized, Weighted Least Squares Estimation

2010 ◽  
Vol 2010 ◽  
pp. 1-7 ◽  
Author(s):  
Chikayoshi Sumi
Keyword(s):  
Least Squares ◽  
Spatial Resolution ◽  
Soft Tissues ◽  
Displacement Vector ◽  
Weighted Least Squares ◽  
Strain Tensor ◽  
Estimation Method ◽  
Modulation Method ◽  
Value Decomposition

Recently, work in this group has focused on the lateral cosine modulation method (LCM) which can be used for next-generation ultrasound (US) echo imaging and tissue displacement vector/strain tensor measurements (blood, soft tissues, etc.). For instance, in US echo imaging, a high lateral spatial resolution as well as a high axial spatial resolution can be obtained, and in tissue displacement vector measurements, accurate measurements of lateral tissue displacements as well as of axial tissue displacements can be realized. For an optimal determination of an apodization function for the LCM method, the regularized, weighted minimum-norm least squares (WMNLSs) estimation method is presented in this study. For designed Gaussian-type point spread functions (PSFs) with lateral modulation as an example, the regularized WMNLS estimation in simulations yields better approximations of the designed PSFs having wider lateral bandwidths than a Fraunhofer approximation and a singular-value decomposition (SVD). The usefulness of the regularized WMNLS estimation for the determination of apodization functions is demonstrated.

scholarly journals Determination of pressure in the near-ground space pile terminated and broadening of the surface

2018 ◽  
Vol 251 ◽  
pp. 04062
Author(s):  
Natalia Kupchikova
Keyword(s):  
Numerical Modeling ◽  
Circular Cross Section ◽  
Analytical Form ◽  
Soil Mass ◽  
Software Systems ◽  
Discrete Method ◽  
Building Foundation ◽  
Geological Conditions ◽  
Complex Engineering

The article deals with the problem of determining the stress state of a complex pile structure with end broadening in the form of a sphere in the soil mass in the analytical form by a discrete method. The calculation schemes for determining the stress tensor at the boundary of the pile of square and circular cross-section with expansions in the soil massif are shown. The elements of the polynomial are found by the discrete method in rectangular and spherical coordinates, which is a cumbersome complex mathematical apparatus for a modern design engineer. The stresses are determined. At present, as the analysis has shown, the solution of complex geotechnical problems of soil bases and foundations for different types of loads in numerical modeling is carried out using modern software. Numerical modeling and calculation with the help of specialized software systems allows to consider the system “building-foundation-ground foundation”, as dynamic, integrally developing. However, the interaction of the components of this system requires a theoretical justification of the resistance of foundations in the ground environment, especially in complex engineering-geological conditions.

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