Radial Stress Components Research Articles

DYNAMIC STRESS ANALYSIS OF A ROTATING SOLID DISC SUBJECTED TO CYCLIC ROTATIONS

This paper presents an analysis of the dynamic stress in a solid disc subjected to cyclically varying rotations with respect to time, that is, Ω^- (t^-) = Ω^-0 + Ω^-1 sin(Ω^-2 t^-) (Ω^-0, Ω^-1, Ω^-2 : constants) The radial displacement and stress components are derived from a general solution for a solid disc, which was obtained previously by the author. A dynamic solution leads to the existence of the two kinds of resonance circular frequencies. For Ω^-1≠0 and Ω^-0=0, the resonance circular frequency Ω^-2 agrees with half of λn which corresponds to the eigen-circular frequencies for in -plane vibrations of rotating discs. for Ω^-1 ≠0 and Ω^-0≠0, Ω^-2 agrees in both cases, λn and λn/2. It is finally discussed how the circular frequency Ω^-2 influences the stress components and their distributions.

Casimir stress in spherical media when εμ = 1

The radial and azimuthal stress components of the electromagnetic zero-point field are calculated inside and outside a spherical surface dividing two media of permeabilities μ1 and μ2. The corresponding permittivities ε1 and ε2 are such that εμ = 1 everywhere. Schwinger's source theory is used. In the inside region all stress components are negative, corresponding to a negative pressure. In the outside region the signs of the angular stress components are reversed, similar to the case for the energy density.

Interfacial Matrix Stresses in Composites Due to Misfitting Cylindrical Constituents

The constituent phases in composite materials of all types can induce local residual stress due to their differing mechanical responses. Changes in thermal, mechanical, or chemical states, encountered in processing or service applications, will generate these stress fields. Analytical solutions to isolated spherical or cylindrical inclusions exist, but the interaction of stress fields among neighboring constituents has not been examined in detail. The present study examined the matrix stress fields at the interface between the matrix and hexagonal arrays of misfitting cylinders. Stresses were analyzed using the photoelastic method, wherein the matrix was the photoelastic material. As the nearest-neighbor cylindrical inclusions first approach each other, there is a tendency for both radial compression and tensile hoop stress components to increase beyond values predicted for single, isolated inclusions. At nearest-neighbor separations less than 40% of the cylindrical inclusion diameter, however, the contact pressure between reinforcement and matrix decreases. At the same time, the tensile hoop component in creases markedly, less so in the hexagonal array than for two inclusions. The physical positioning and arraying of the reinforcement will clearly determine the local stress in duced by processing, which, in turn, will influence composite response and service endurance.

Stress distribution in cylindrical windows for optical high-pressure cells

Calculations are described of the stress distribution in optical high-pressure windows consisting of a transparent cylinder which is supported by a plug bearing a hole as optical aperture. The method based on an extension of Love’s strain function, the Galerkin vector, takes advantage of the axisymmetry of the arrangement, thus allowing very economic computations. The results apply to homogeneous, isotropic materials in the linear-elastic region. Critical stress concentrations exist at the unsupported area, as the radial stress component will most probably become positive there and near the edge of the support where the maximum shear stress occurs. It is shown that, in general, thickness to diameter ratios greater than 0.5 will not improve the pressure resistance of the window significantly.

Measurement of a Stress Gradient through the Bulk of an Aluminum Alloy Using Neutrons

Neutron diffraction has been employed to measure an applied stress gradient through the bulk of a 25.4 mm thick aluminum alloy bar. The experiment was designed to test the feasibility of combining the penetrating power of neutrons with the residual stress measurement methodology developed for near-surface regions using X-rays. The load was applied on a curved beam sample so that the tangential stress (σ θ) ranged from +302.4 MPa (+43851 psi) to −413.7 MPa (−60000 psi). A small radial stress component (σ r) was also present. Three methods of measurement were employed which enabled gradients ofσ θ –σ r/v,σ θ, andσ θ –σ r to be measured(v is Poisson’s ratio) through the sample. Two diffraction peaks, 311 and 333/511, were used. The depth of gradient sampled at each point ranged nominally from 2 to 7 mm; however, the effective depth sampled ranged from 1 to 3 mm. Experiment and theory are in reasonable agreement, suggesting that the method has potential.

A Thermoelastic Analysis of Dislocation Generation in Pulled GaAs Crystals

The optical and electronic characteristics of devices based on GaAs (LEDs, laser diodes, etc.) are adversely affected by the dislocations originating in the substrates. We demonstrate by means of thermoelastic analysis that the primary cause for the observed dislocation density patterns in Czochralski-pulled GaAs single crystals, which serve as a source for substrates, is crystallographic glide, induced by the excessive thermal stresses arising during the growth process. First, we formulate a tractable model for crystal growth. We obtain the temperature distribution in the crystal by solving the quasi-steady-state partial differential equation for heat conduction subject to appropriate boundary conditions. The closed-form solution includes time, pull rate, axial location, radius, convective and radiative heat transfer coefficients (h r + h c ), and a fixed ambient temperature (T a ) among the variables. Next, from the temperature profiles we determine the radial, tangential, and axial stress components acting on the GaAs boule. These stresses permit the evaluation of the 12 resolved shear stress components for the {111}, 〈1b10〉 slip system. We postulate the sum of the absolute values of the 12 components (σ tot ) to be proportional to the dislocation density within an additive constant. Employing σ tot as a parameter, we have constructed dislocation distribution contour maps for {100} GaAs wafers which are in good accord with the dislocation patterns observed on KOH-etched wafers cut from near the top end of Cr and Te-doped GaAs boules. A detailed examination of the effect of the numerous parameters on the dislocation density of Czochralski-pulled GaAs is also given. Only by a drastic increase of T a and a substantial decrease of h r + h c would one be able to overcome the natural limitations imposed by the thermal and mechanical properties on dislocation density. Finally, we pay attention to the effects of elastic anisotropy and interfacial heat flux, discuss the philosophical and mathematical difficulties associated with finding a true transient solution, provide some practical suggestions

コアディスキング現象に関する研究

Discing of rock cores refers to the formation of discs of relatively uniform thickness which fracture on surfaces approximately normal to the axis of the core. The purpose of the present paper is to study the mechanism of this phenomenon which is best observed when drilling into highly stressed hard rock.For the purpose of the theoretical study, the state of stress in the region where core discing initiates has been analyzed through the use of Finite Element Method and the results of this analysis have been compared with the stress conditions, as determined experimentally, required to produce core discing in specimens subjected to the axial stress Pz and the radial biaxial stresses Px and Py. This comparison show the discing initiates not at the bottom of kerf area but at the root of the core where subjected to the maximum tensile stress σz, across a plane perpendicular to the axis of the core, which increases as radial stress component 1/2 (Px+Py) increases and diminishes with increasing axial stress Pz. Moreover, the magnitude of this tensile stress, as determined analytically, is fairly equal to the Brazilian tensile strength St. As the result of above investigations, the relationship among the stresses Px, Py and Pz required to occur discing, is determined, that is1/2 (Px+Py)≥-4St+Pz, 2.5≥Px/Py≥0.4Moreover, the authors have studied on the practical implications of core discing and on the similar fracture of the hollow core which could be obtaind by the over drilling, with the same axis to the previous drilling. It is experimentally comfirmed the lower stress conditions of hollow core discing than the usual and its conditions are mainly concerned with the ratio of diameters. Finally, it is pointed out that the application of these phenomena to determine the rock stress is quite possible.

Stress Relaxation in Press-Fitted Joints

When contact pins, wire wrap posts, etc., are press fitted into printed circuit boards, the contact force at the interface of a post and plate relaxes with time. Much of the relaxation of the contact force occurs immediately after the connection has been made. Theoretical estimates on the reduction in contact force until a steady state (a steady state is assumed to be reached when the stress rates become 1 percent of their initial values) is reached are presented. Since most of the relaxation of the radial stress component occurs in the vicinity of the hole, the effect of adjacent joints on the relaxation characteristics of a joint are neglected. And, therefore, only an idealized geometry of a thin circular plate with a single press-fitted hole is considered.

Experimental Investigation of Hydraulic Fracturing Through Perforations

In this study it was found that breakdown pressures of hydraulic fractures decrease as the number of perforations increases. The existence of the casing and the perforations seems to have little influence on the direction of the created fracture, which is perpendicular to the least principal stress. Introduction The majority of hydraulic fracturing treatments in the oil and gas fields are performed through perforations. These perforations are usually created by perforations. These perforations are usually created by shaped charges, by hydrojets, or occasionally by bullets. They generally penetrate through the casing, through the cement, and several inches into the formation. Each perforation has approximately a cylindrical shape, with a diameter of about 1/8 to 1/2 in. Most of the known theoretical and experimental research on hydraulic fracturing has been performed in open holes. The reasons for this are that the openhole situation is easier to handle, and more important, the studies on open holes provide insight into the more complicated problem of fracturing cased holes. This paper appears to be the first known serious examination of hydraulic fracturing through perforations. Because of a lack of knowledge about the perforations. Because of a lack of knowledge about the stress concentrations around the borehole and the perforations, the studies reported here are mainly perforations, the studies reported here are mainly experimental and composed of observations of the types, orientations, and breakdown pressures of the induced fractures. The theoretical examination of the problem is limited to the calculation of the stresses around the casing and in the formation. However, the experimental results are quite interesting and shed new light on the influence of perforations on the created hydraulic fractures. Stress Distribution Around Cased Boreholes It is generally accepted that hydraulic fractures are created whenever the maximum tensile stress induced at the borehole wall exceeds the tensile strength of the formation. Thus the study of stress distribution around the borehole becomes an integral part of the examination of fracture initiation. Contrary to openhole situations, it is very difficult to derive analytical expressions for the stress distribution around perforated cased holes, mainly because of the complicated geometry. Thus, in examining the fracture initiation in cased holes, the only two alternatives appear to be experimentation or numerical simulation. The results reported here are derived from an experimental approach. The problem of stress distribution around a cased hole (without perforations) has been solved by Savin, for the generalized plane stress or plane strain conditions. Fig. 2 compares the stresses around open and cased holes. The symbols sigma 11, sigma 22, and sigma 33 denote the three in-situ principal stresses, and sigma, sigma 33, and sigma are used for the tangential, radial, and shear stress components around the borehole (Fig. 1). The borehole is assumed to be parallel to sigma 33. The curves in Fig. 2 show that the existence of the casing significantly alters the stresses induced by sigma 11, sigma 22, and sigma 33 around the borehole. When one adds to this the changes caused by the perforations and fluid leak-off, it becomes obvious why the breakdown pressure of perforated cased holes should be considerably perforated cased holes should be considerably different from that of open holes, JPT P. 1201

Inclusions in Laser Materials.

One of the severe problems encountered in high-power-solid-state laser systems is the thermal damage to laser rods and optical elements. One such type of damage is thought to arise from metallic or dielectric inclusions; i.e., impurities with physical and optical properties which differ substantially from those of the host material. Such inclusions may absorb an appreciable amount of the incident radiation and thereby may undergo thermal expansion. This produces major stresses within the host material. Estimating such thermal properties requires the consideration of solutions to the heat diffusion equation and to the thermal stress equations with appropriate boundary conditions. The optical path length change for a probing light ray passing near the inclusion, the radial and tangential stress components, and the changes of the refractive index for radially polarized and tangentially polarized light due to the thermal stress field are computed. The dependence of the maximum value of the tensile stress upon the size of the inclusion and upon the physical properties of the host is examined. The feasibility of using optical techniques to detect metallic and dielectric inclusions in laser materials before they cause damage also is studied. The computations suggest that the use of laser pulse widths of the order of microseconds or longer may be more promising for the detection of small incipient absorbing centers than the use of nanosecond pulse widths.

Equilibrium flow of a general fluid through a cylindrical tube

AbstractEquilibrium flow of a general fluid through a long, straight, cylindrical tube is examined, and equations are derived for determining the three pertinent material functions, the shear stress component, the difference between the radial and angular normal stress components, and the difference between the axial and angular normal stress components. These equations are expressed in terms of quantities which are measurable. Experimental data are obtained for a polymer solution, and the material functions are calculated.

Flexural Stresses in Curved Beams of I- and Box-section

A mathematical and experimental investigation is made of the stresses resulting from the flexure of curved beams of I- and box-section. It is shown that the flanges, if unsupported, distort under the influence of radial stress-components, and are less effective in carrying the circumferential bending stresses than would appear from ordinary methods of calculation. The distortion is accompanied by transverse bending stresses which, in certain circumstances, may be of greater magnitude than the circumferential stresses, and which at the inner radius combine with the circumferential stresses to introduce critical stress conditions. The distortion effects may be limited by using thick, narrow flanges, by ample fillets between the flanges and the webs, by radial gussets and by suitable disposition of the webs in box-sections. Formulae and charts for the estimation of stresses are presented in convenient form for design purposes.