Three-dimensional local stress analysis on grain boundaries in polycrystalline material

In order to understand the initiation behavior of microstructurally small cracks in a stress corrosion cracking condition, it is important to know the tensile normal stress acting on the grain boundary (normal GB stress). The local stress in a polycrystalline body is enhanced by the inhomogeneity which stems from the shape and orientation of each grain. The stress in a three-dimensional polycrystalline body consisting of 100 grains with random orientation, under a remote uniform tensile stress condition, is evaluated by the finite element method. It was revealed that the local stress on the polycrystalline body is inhomogeneous under uniform applied stress and becomes large at those grain boundaries that are perpendicular to the load axis, though there is large fluctuation. It was also shown that the normal GB stress tends to be large near the triple points due to the deformation constraint caused by adjacent grains. Finally, the maximum stress on the surface of a large component caused by the inhomogeneity was evaluated by using Gumbel statistics.     

Large-scale structure of a leading-edge separation bubble with local forcing

The Karhunen-Loeve (K-L) expansion is used to extract coherent structures from a leading-edge separation bubble with local forcing. A leading-edge separation bubble is simulated using the discrete vortex method, where a time-dependent source forcing is perturbed near the separation point. Based on the wealth of numerical data, the K-L procedure is applied in a range of the forcing amplitude (A₀ = 0, 0.5, 1.0 and 1.5) and forcing frequency (0 f_FH/U_∞ 0.3). Application of K-L procedure reveals that the eigenstructures are changed noticeably by local forcings. In an effort to investigate the mechanism of decreasing reattachment length (x_R), dynamic behaviors of the expansion coefficients and contributions of the eigenfunctions are scrutinized. As the forcing amplitude increases, large-scale vortex structures are formed near the separation point. Furthermore, the flow becomes more organized, which results in the reduction of x_R. Two distinctive regimes are classified: the regime of decreaing x_R and the regime of increasing x_R. The K-L global entropy indicates that x_R is closely linked to the organization of the flow structure.     

Existence and nonuniqueness of local separation zones in viscous jets

The plane steady problem of the flow of a viscous wall jet past a smoothed break in the contour of a body is considered. For convenience, the flow in the neighborhood of the junction between two flat plates inclined at an angle to each other is chosen for study. As a result of the small extent of the region investigated the flow field is divided into two layers: the main part of the jet, which undergoes inviscid rotation, and a thin sublayer at the wall, which ensures the satisfaction of the no-slip condition. Particular interest attaches to the flow regime in which the solution in the sublayer satisfies the Prandtl boundary layer equations with a given pressure gradient. A similar problem was studied in [1–4]. The present case is distinguished by the structure of the free interaction region in a small neighborhood of the point of zero surface friction stress. By means of the method of matched asymptotic expansions, applied to the analysis of the Navier-Stokes equations, it is established that the interaction mechanism is that described in [5–7]. As a result, an integrodifferential equation describing the behavior of the surface friction stress function is obtained. A numerical solution of this equation is presented. The range of plate angles on which solutions of the equation obtained exist and, therefore, flows of this general type are realized is determined. The essential nonuniqueness of the possible solutions is established, and in particular attention is drawn to the possible existence of six permissible friction distributions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 38–45, January–February, 1986.The author wishes to thank V. V. Sychev and A. I. Ruban for their useful advice and discussion of the results.     

Three-dimensional separation in the neighborhood of roughness on the surface of an axisymmetric body

Steady-state viscous incompressible fluid flow past an axisymmetric slender body is considered at high Reynolds numbers in the regime with vanishing surface friction in a certain cross-section. In a small neighborhood of this cross-section interaction between the boundary layer flow and the external irrotational stream develops. In order to study the structure of the three-dimensional flow with local separation zones it is assumed that there is three-dimensional roughness on the surface of the body with the scale of the interaction zone. For this zone a numerical solution of the problem is obtained and its nonuniqueness is established. The surface friction line (limiting streamline) patterns with their inherent features are constructed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 67–79, May–June, 1995.Thus, on the basis of the asymptotic marginal separation theory it is possible to obtain fairly simple solutions describing flows with a complex surface friction line structure.     

Propagation of slip pulse along frictionless contact interface with local separation between two piezoelectric solids

The Stroh formalism of piezoelectric materials,Fourier analysis and singular integral equation technique were used to investigate the existence of a pulse at the fric- tionless interface in presence of local separation between two contact piezoelectric solids. The two solids were combined together by uniaxial tractions and laid in the electric field. The problem was cast into a set of Cauchy singular integral equations,from which the closed-form solutions were derived.The numerical discussion on the existence of such a slip pulse was presented.The results show that such a slip pulse,which has square root singularities at both ends of the local separation zone,can propagate in most material combinations.And the existence of such a slip pulse will not be affected by the applied mechanical and electric fields in some special material combinations.     

Three-dimensional Gouyon waves

Three-dimensional steady-state periodic waves in deep water with weak (of order of the wave amplitude) vorticity are considered. The solution describing the wave properties is constructed by the perturbation theory method in modified Lagrangian coordinates. The wave structure and dispersion properties are found correct to the square of the wave amplitude.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 125–130, July–August, 1996.     

Three-dimensional shock intersection

The flow field in the neighborhood of the three-dimensional intersection of two shocks of different families is investigated when in the plane perpendicular to the line of intersection the flow velocity component is subsonic behind at least one of the departing shocks. In the plane case these flows are not realized. The boundary of the domain of the key parameters for which these flows are possible is determined. The characteristics of the flow field are determined when: (1) behind the departing shocks the flow is homogeneous, and (2) the velocity vectors behind the departing and arriving shocks are parallel to a single plane which contains the intersection line. The flow in Mach-type shock intersection in the neighborhood of the intersection lines (triple points in the plane) is a particular case of the problem considered. It is shown that Mach-type shock intersection is not possible when the intensity of the arriving shocks is less than for their steady-state Mach intersection in the calculation plane. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 137–143, November–December, 1998.     

Three-dimensional crack analysis

A method is presented for the stress analysis of plane cracks of any shape in a stressed three-dimensional linear elastic space. The approach utilizes a system of integral equations which is defined over the crack area only. When these equations are solved for the unknown dislocations, all other quantities related to the crack and the space can then be found. The text contains sections concerning equation system derivation, numerical procedures, stress intensity factors, rectangular cracks, and earthquake control.     

Three-dimensional non-isothermal extrusion flows

A three-dimensional (3-D) non-isothermal study of viscous free-surface flows with exponential dependence of viscosity on temperature is presented. The effects of non-isothermal conditions and/or geometry on the extrudate shape are investigated with a fully three-dimensional finite element/Galerkin formulation. Apart from the well known thermally induced extrudate swelling phenomenon, bending and distortion of the extrudate may occur because of temperature differences and/or geometric asymmetries. A temperature difference across the die can be imposed by heating or cooling the die walls, but can also arise because of asymmetric viscous heat generation due to the die geometry. Temperature differences affect velocity profiles because of the temperature dependence of viscosity and lead to extrudate bending, an effect known as kneeing in the fiber spinning industry. It is also shown numerically and confirmed experimentally that the die geometry induces extrudate bending even in the case of isothermal Newtonian flows.     

Three-dimensional supersonic internal flows

In order to examine the transition between regular and Mach reflection in a three-dimensional flow, a range of special geometry test pieces, and inlets, were designed. The concept is to have a geometry consisting of two plane wedges which results in regular reflection between the incident waves off the top and bottom of the inlet capped by two curved end sections causing Mach reflection. The merging of these two reflection patterns and the resulting downstream flow are studied using laser vapor screen and shadowgraph imaging supported by numerical simulation. An angled Mach disc is formed which merges with the line of regular reflection. A complex wave pattern results with the generation of a bridging shock connecting the reflected wave from the Mach reflection with the reflected waves from the regular reflection. In order to experimentally access the flow within the duct, a number of tests were conducted with one end cap removed. This resulted in a modified flow due to the expansive flow at the open end the influence of which was also studied in more detail.     

Three-dimensional modeling of tires

Modeling the stress-strain state of pneumatic tires in the conditions of steady-state and transient rolling is of interest for mechanics of composites and computational mechanics and important from the applied point of view. Mechanical models of various levels of complexity can be used for numerical modeling. In quite a few papers, the corresponding models are derived from the theory of orthotropic shells [1]. However, more thorough and accurate studies of the stress-strain state can be carried out on the basis of three-dimensional models based on the elasticity or viscoelasticity equations. As far as Russian authors are concerned, this approach has first been suggested and implemented in [2]. Another, combined approach uses both the shell theory and the three-dimensional equations of elasticity theory [3, 4]. This approach is reasonable, because the tire structure includes both volumes filled with rubber and thin layers of the rubber cord. The rubber cord layers can be considered as a composite whose structural components possess very different properties. Also, it is quite admissible to consider the rubber cord as a structure periodic in the horizontal projection. Note that the mathematical theory of periodic composites has been developed in [5]. Owing to strong anisotropy and inhomogeneity of the material, large shape distortions of the tire, and, in some cases, its large deformations, viscoelastic properties of rubber play an important role, so that the mechanic model of the tire turns out to be quite complex. The large property differences between various structural components make the matrix of the resulting system of linear equations ill-conditioned, which complicates its numerical solution [6].In this paper, theoretical aspects of a three-dimensional tire model and its numerical implementation are considered.     

Three-dimensional periodic boundary layers

Summary Three-dimensional periodic boundary layers on an arbitrary surface are considered assuming that the outer flow is a known periodic potential flow. It is shown that, if the Strouhal number and the Reynolds number are of the same order and if both are large, the interaction between the curvature of the surface and viscosity induces a harmonic part in the secondary motion inside the boundary layer in addition to steady and subharmonic parts.

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Übersicht Es werden dreidimensionale periodische Grenzschichten an einer beliebigen Oberfläche betrachtet unter der Annahme, daß die Außenströmung eine bekannte periodische Potentialströmung ist. Es wird gezeigt, daß unter der Vorsausetzung, daß Strouhalzahl und Reynoldszahl groß und von gleicher Größenordnung sind, durch das Zusammenwirken von Oberflächenkrümmung und Zähigkeit innerhalb der Grenzschicht ein harmonischer Anteil für die sekundäre Strömung innerhalb der Grenzschicht entsteht, der sich den stationären und den subharmonischen Anteilen überlagert.

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The author thanks Prof. S. D. Nigam for his comments on the first draft of the paper.     

Three-dimensional analysis on plates

I.IntroductionGenerally,asathree-dimensionaI(3-D)solid-theplateshouldbeanalysedwiththethickplatetheory.Thethickplatetheoryismultifarious:Acust0marythick[heoryoriginatesfromvariousmodificationsofthethinplatetheory,whichisbasedonKirchhoffLovehypothesis'with…     

Three-dimensional, three-component wall-PIV

This paper describes a new time-resolved three-dimensional, three-component (3D-3C) measurement technique called wall-PIV. It was developed to assess near wall flow fields and shear rates near non-planar surfaces. The method is based on light absorption according to Beer–Lambert’s law. The fluid containing a molecular dye and seeded with buoyant particles is illuminated by a monochromatic, diffuse light. Due to the dye, the depth of view is limited to the near wall layer. The three-dimensional particle positions can be reconstructed by the intensities of the particle’s projection on an image sensor. The flow estimation is performed by a new algorithm, based on learned particle trajectories. Possible sources of measurement errors related to the wall-PIV technique are analyzed. The accuracy analysis was based on single particle experiments and a three-dimensional artificial data set simulating a rotating sphere.     

Turbulent separation flows

Turbulent separation flows arise when objects move in the oceans and in the atmosphere, and also when a liquid or gas flows past elements of the Earth's relief, technological and industrial plant, and constructional elements. Therefore, problems of turbulent separation flows cover the entire range of velocities of continuum motions and under such varied boundary conditions that the forms, properties, and manifestations of turbulent separation are inexhaustible. The aim of the present paper is to discuss the available results and the possibilities for further development of computational models of turbulent separation flows. The somewhat nominal classification of such models given in the paper reflects essentially the sequence of their historical development.Paper presented at Fifth All-Union Symposium on Theoretical and Applied Mechanics, Alma-Ata, 1981.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 31–47, March–April, 1982.