Showing papers on "Stress field published in 1970"

Limit analysis of plane problems in soil mechanics

Abstract: A computer method is developed for failure analysis of plane problems in soil mechanics. It is assumed that the soil obeys the Mohr-Coulomb failure criterion and that all stresses vary linearly within each element of a triangular mesh which spans the zone under investigation. An optimal statically admissible stress field corresponding to a lower bound solution is isolated by the method of linear programming. The method has been applied to several bearing capacity and earth pressure problems.

Geometric Design of Composite Cylindrical Characterization Specimens

Abstract: The stress field within a highly anisotropic cylinder, even under simple loading conditions, is far from uniform. Thus, like other verbage which has its origins in the stress analysis of isotropic bodies, the terminology "thin-walled cylinder" must be redefined for aniso tropic materials, and is a strong function of elastic moduli. This places a severe burden on the experimentalist who must employ such specimens to characterize composite materials under biaxial states of stress. In this work, a procedure is outlined to determine the proper geometry of anisotropic and laminated cylinders such that elastic stress gradients can be reduced to a predetermined limit. The ap proach consists of combining a modified plane strain elasticity solu tion with shell theory. Parametric studies on materials possessing high and low degrees of anisotropy indicate general guidelines for proper tube geometry for precise characterization under simulated laboratory loading and clamping conditions.

Elastic Fields and Energies of a Circular Edge Disclination and a Straight Screw Disclination

Abstract: The displacement and stress fields for a circular edge disclination are derived from Green's tensor function. The elastic strain energy of this circular edge disclination is calculated and compared with the energy of two different kinds of circular dislocation loops. Finally, the stress field and elastic strain energy of a straight screw disclination is computed and is compared to the case of a straight screw dislocation.

Seismic radiation from explosions in prestressed media and the measurement of tectonic stress in the Earth

Abstract: The radiation field from explosions in a prestressed medium can be theoretically predicted on the basis of a dynamical theory of stress relaxation in the vicinity of the shock-induced fracture zone created by an explosion. The field consists of the normal compressional wave field resulting from the conversion of the shock wave to an elastic wave plus an anomalous part due to the release of strain energy. In this study we consider the nature of the radiation field to be expected from such a source in an inhomogenous earth and determine the stress field required to explain the observations from a large underground explosion. The field is described in terms of radiation patterns as functions of frequency or alternately as the amplitude and phase spectrums at particular distances. These theoretical predictions are compared to the Love- and Rayleigh-wave radiation patterns and spectra from the nuclear explosion Bilby. Using the known source parameters, we obtain agreement between the observed radiation patterns and the predicted patterns for a pure shear prestress field equivalent to a shear couple oriented approximately N10°W. Using the amplitude spectrum of the observed field adjusted for propagational effects, we find that the prestress was 70 ± 20 bars in the source area. We conclude that this approach can be utilized as a means of systematically measuring the stress field of the earth.

Elastic Field of a Point Defect in a Cubic Medium and its Interaction with Defects

Abstract: Three equal orthogonal double forces without moment aligned along the cubic axes are used as a model for a point defect in a cubic medium. The method of Fourier transforms is used to obtain the solution for the displacement and stress fields. The solution is presented in a polynomial form. The elastic interaction between a point defect and an edge dislocation is computed for copper by making the displacement of the edge dislocation against the stress field of the defect. The interaction with the physically significant [112] edge dislocation on the (111) plane in copper is presented. The computer program was verified by the agreement of its results with those for the hypothetical [001] edge dislocation on the (010) plane, for which the stresses can be calculated in closed form. Near the slip plane, the calculated anisotropic interaction was almost twice that of a corresponding isotropic one. The elastic interaction between two point defects in copper is calculated, indicating regions of attraction of like defects along the cube axes and repulsion along the cube diagonals. Eshelby's perturbation analysis for materials with slight anisotropy predicts qualitatively similar effects, but the repulsion is much greater than that predicted by his approximate analysis.

Craze distribution around cracks in polystyrene

Abstract: The distribution of surface crazes in the vicinity of a stationary edge crack in a polystyrene sheet in tension is compared with the stress fields already investigated experimentally by Post. It is shown that the extent of crazing corresponds closely with the maximum principal stress contours determined experimentally and that the shapes of the crazes indicate that they grow along directions parallel to the minor principal stress axis.

Stress concentration in silicon-insulator interfaces

Abstract: Edges of silicon oxide or nitride diffusion masks produce in the silicon substrate stresses of thermal or intrinsic nature. When the stress field is evaluated in terms of an elastic two-dimensional model, with the proper boundary conditions, stresses attain a maximum value of the order of 10 9 dy/cm 2 . The shear component is particularly important. Experiments with monochromatic infra-red transmission are reported. They show a marked anomaly in transmittance in the region near the mask edge, where stresses are presumably large. To the first order this anomaly appears to be caused by a piezo-absorption phenomenon. The implications of the large stress field for semiconductor device behavior are analyzed qualitatively, while the limitations of the calculations caused by limitations in the model, are emphasized. These results nevertheless, on balance, point to the serious possibility that some reported phenomena in semiconductor devices can be understood as edge-stress dependent processes.

Three-dimensional stress distributions around a cylindrical hole and anchor

Abstract: STUDIES HAVE BEEN CONDUCTED ON THE STRESS DISTRIBUTION AROUND A CYLINDRICAL HOLE IN A TRIAXIAL STRESS FIELD TOGETHER WITH THE CASE OF A LOADED ANCHOR FILLING THE HOLE. THE ANCHOR WAS LOADED BOTH IN COMPRESSION AND TENSION. THE STRESS CONCENTRATION FACTORS ON THE END OF THE HOLE DUE TO AXIAL AND RADIAL STRESSES, WHICH ARE OF INTEREST IN INTERPRETING STRAIN RELIEF MEASUREMENTS IN DRILL HOLES AS WELL AS IN EXAMINING ANCHOR STRESSES, ARE SHOWN TO VARY WITH POISSON'S RATIO. EXPERIMENTALLY DETERMINED FACTORS ARE FOUND TO BE SCATTERED AROUND THE CURVE OF VARIATION FOUND IN THIS WORK. THE NATURE OF THE TRANSMISSION OF LOAD FROM A COMPRESSION ANCHOR TO ROCK IS SHOWN TO VARY, AS HAD BEEN PREDICTED QUALITATIVELY, WITH THE RATIO OF THE MODULUS OF DEFORMATION OF THE ANCHOR TO THAT OF THE ROCK MASS. THE PROPORTION OF THE LOAD, TRANSIMITTED THROUGH BEARING ON THE BOTTOM OF THE ANCHOR, INCREASES WITH THE RATIO OF THE MODULI. TENSION ANCHORS CAN PRODUCE LARGE TENSILE STRESSES IN THE ROCK, WHICH MAY ACCOUNT FOR SOME OF THE COMMONLY OBTAINED INITIAL CREEP. /AUTHOR/

Stress Analysis Based on Albite Twinning of Plagioclase Feldspars

Abstract: Plagioclase twins mechanically on the albite law. Twinning is most likely to occur when the resolved shear stress on the twin plane, (010), and in the glide direction, perpendicular to [100] in (010), is at a maximum. Only those crystals oriented in the stress field to approximately meet this condition will twin. Thus, in a rock containing mechanically twinned grains, the principal stress directions affecting the rock may be approximated by measuring the twin elements of these grains. The plagioclase fabric must be taken into account if the results are to be significant. Study of samples of anatectic granodiorite of the Chewack River Gneiss in the northeastern Cascade Range, Washington, where the unit was deformed adjacent to the Chewack-Paysaten fault, demonstrate the use of the method.

A fractographic study of Stage I fatigue cracking in a nickel-base superalloy single crystal

Abstract: An electron fractrographic study was made of opposing crystallographic (Stage I) fatigue fracture surfaces of specimens of a single crystal nickel-base superalloy, low carbon MAR-M200, that were tested at room temperature. In regions near the crack initiation site, features on both surfaces are the same. In regions at some distance from the initiation site significant differences in the type and extent of microfeatures were observed. For a crack propagating in an upward direction, irregular markings were observed on the upper fracture surface and regularly spaced slip offsets and slip band cracks were observed on the lower surface. These observations are explained by a consideration of the elastic stress field and the resultant glide forces on all possible slip systems surrounding a crack growing at an angle to the principal stress direction. Additionally the results are used to support a previously proposed model for Stage I fatigue crack propagation.

Solid-Solution-Hardening of Tantalum-Base Alloys

Abstract: Solid-solution-hardening has been studied on single crystals of TaRe, TaW, TaMo, and TaNb with a fixed solute concentration of 3·5 at.-%. The critical resolved shear stress was measured over the temperature range 77–2000 K. It is found that ∆τ0, the difference in shear stress between the alloy and the pure tantalum, exhibits a plateau range between 1000 and 1500 K. The modulus misfit parameter ɛ G (K33), derived from the modulus that determines the stress field of a screw dislocation, is shown to be a very good parameter to describe solid-solution-hardening in tantalum.

Influence of stress interaction effects upon pore motion in solids.

Abstract: A computer oriented analysis was undertaken in an attempt to fix the sign and magnitude of the response of a pore to a stress field. The present work agrees very well with an analytical result of other authors for the interaction of two bubbles within a solid continuum and reasonably well with their approximate analytical result for the interaction between a bubble and a free surface. The interaction between a bubble and a clamped surface is obtained. Two bubbles will always attract as long as at least one contains some “uncompensated” pressure. Further, such a bubble will be attracted to a free surface and repelled from a clamped surface. An analytical solution to the problem of an equilibrium bubble placed in a linear uniaxial stress gradient indicates the bubble will move up the gradient, whether the gradient is produced by external tension or compression. This is compared with a previous result for a pressure gradient; the uniaxial stress gradient produces a force about 50% higher than that due to a pressure gradient. Finally, estimates are made for the magnitude of these forces under physically plausible conditions.

Long range elastic interaction of prismatic dislocation loop with a grain boundary

Abstract: The expressions for the displacement and the stress field around a prismatic infinitesimal dislocation loop lying near the welded boundary and for the displacement field near the slipping boundary are given. The expression for the total force by which the loop is either attracted or repelled from the grain boundary (welded or slipping) was calculated. The forces are graphically illustrated for different combinations of material constants. The calculations were carried out within the isotropic elasticity.

Dislocation behavior at tilt boundaries of infinite extent

Abstract: A detailed theoretical analysis has been made of the stress fields which arise from the motion of glide dislocations across a symmetric tilt boundary. These stress fields are long range and result from the formation within the boundary of virtual grain boundary dislocations. A similar type of long range stress field is generated when two crystals of differing lattice size are joined together. In the former case the long range stress fields may be sufficient to generate dislocation glide loops while in the latter case these loops are of the prismatic type and move by climb. Portions of both types of loops move to the boundary and become incorporated into them as interface dislocations, in turn reducing the long range stress fields arising from the virtual dislocations.

Gravitational stress field around a tunnel in soft ground

Abstract: The finite element method has been used for determining the stress distribution and the displacements due to gravity around an unlined tunnel driven through a semi-infinite medium, characterized by three idealized material behaviors reflecting approximately a short term behavior of natural undisturbed insensitive and sensitive clays. The knowledge of stress and displacement fields around an unlined tunnel can be used for evaluating the need for supports according to the acceptability of expected deformations.

Exponentially Decaying Pressure Pulse Moving With Constant Velocity on the Surface of a Layered Elastic Material (Superseismic Layer, Subseismic Half Space)

Abstract: : The response of a layered elastic half-space to a progressing exponentially decaying normal surface pressure is evaluated for a case in which the constant velocity V of the moving pressure is greater than that of the P and S waves, respectively, in the upper layer (superseismic) and smaller than these wave speeds in the underlying half-space (subseismic). It is assumed that a steady-state exists with respect to coordinate axis attached to the moving load. The superseismic-subseismic geometry results in a stress field that extends over the entire plane, with sharp shocks possible only in that portion of the layer that lies behind the front of the progressing normal loading. A computer program for evaluating stresses and velocities at points in the medium is available and results are presented for a typical configuration of interest. (Author)

Analysis of Axi-Symmetric Extrusion

Abstract: In the present paper, the axi-symmetric extrusion of the Tresca's solid is analysed by means of the semi-inverse method under the Haar-von Karman hypothesis. At first, the stress field is constructed by assuming the distributions of the pressure and the frictional stress on die surface. Then, the velocity distribution in the slip line field is calculated with the boundary conditions of the velocities of the rigid regions. Here, an arbitrary stream line is considered as the die surface, and the stress and the velocity fields obtained above become the solution of the problem of certain peculiar frictional condition, which is different from the given one. Several iterations of this procedure make the difference sufficiently small. From the numerical calculations, the lower and the upper bounds of the extrusion forces are obtained, which are much better than the usual solutions, and the mean extrusion pressures are found to be 10%∼30% larger than those of the plane strain extrusions. Then the strain distributions are compared with the experimental results analysed by the moire and the gridwork methods.

Stress Distribution Around a Circular Bar, With Flat and Spherical Ends, Embedded in a Matrix in a Triaxial Stress Field

Abstract: Abstract : The report deals with the stress and strain distribution around a circular bar embedded in a matrix and subjected to a mechanically applied triaxial load. The three-dimensional 'freezing' technique of photoelasticity was used. The results obtained correspond to the case of a rigid circular bar embedded in an homogeneous, elastic matrix. Two models were analyzed; in one the axis of the circular bar was parallel to the direction of the loading and in the other the axis of the circular bar was normal to the direction of loading. By combining the results obtained independently for these two cases, stress and strain distribution around the circular bar for various ratios of triaxial load can be obtained. (Author)

Fatigue Crack Propagation in S15C Steel

Abstract: Many studies on fatigue crack propagation have hitherto been presented. Most of them are directed in search of the relation between the crack propagation rate and both the crack length and the applied stress range, that is, the crack propagation law. In one of these laws, the crack propagation rate has been estimated so far with a function of the stress intensity factor K, as the simplest and the most appropriate single variable which represents the elastic stress field around the crack tip. This method of approach is very exact and accurate in such a case as the crack length is short and the applied stress in fatigue is adequately small in comparison with the yielding strength. However, there may be other cases where the choice of K is inappropriate. We need therefore another approach on the basis of the propagation mechanism. Considering that the crack propagation rate can be determined by the distribution of plastic deformation, we have tried to estimate the law with new variables.In this study annealed plane specimens of 0.16% C low carbon steel with a shallow single edge notch were fatigued under completely reversed in-plane bending stress. The plastic deformation near the crack tip was examined by means of an optical microscope and the back-reflection X-ray microbeam Debye technique. The obtained results are summarized as follows:(1) The slip bands zone size ahead of fatigue crack tips is much smaller than the plastic zone size predicted from Dugdale's model. The relation is given by the following equation.ξ/l=0.032{sec(π/2σ/0.77σy)-1}where ξ, 1, σ and σy represent respectively the slip bands zone size, the crack length, the applied stress and the tensile yielding strength. The residual stress induced by fatigue will reduce the size of the plastic zone at the crack tips in cyclic stressing.(2) The crack propagation rate dl/dN is uniquely related to the slip bands zone size ξ ahead of the crack tips, asdl/dN=1.9×10-8ξ1.5regardless of the stress amplitude or the crack length.(3) The excess dislocation density Dm at the fatigue crack tip increses, and the subgrain size t decreases as crack propagation rate dl/dN becomes larger and their relationship is expressed as, dl/dN=5.2×10-30Dm2.6dl/dN=1.7×10-5t-3.3(4) The crack propagation laws estimated with the stress intensity factor are slightly but inevitably dependent on the stress amplitudes. These laws are independent of them, on the other hand, provided that we choose the representative quantities of the plastic deformation, for examples, the plastic zone size, the excess dislocation density or the subgrain size ahead of the crack tip as the single variable.

Elastic properties of dislocations lying in a planar boundary

Abstract: The formulae for the stress field, self-energy and interaction energy of a dislocation lying in a planar boundary between two anisotropic media are given. The solution is applied to the twinning dislocations, especially in bcc metals. A similar solution is also given for a dislocation lying in the boundary between two different isotropic media.

Application Of A Discontinuous Strip Yield ModelTo Multiple Site Damage In Stiffened Sheets

Abstract: Stiffened panels are widely used in aircraft wing and ftiselage structures. As a result of the cyclic nature of the loads associated with each flight, and material and manufacturing defects it is known that wide spread fatigue cracks may develop particularly around high stress regions such as fastener holes. This simultaneous development of relatively small fatigue cracks at multiple sites in the same structural element can give rise to their joining to form one large crack. This main crack, resulting from the multiple site damage (MSD) may cause immediate and complete failure of the structure.The effect of multiple site damage on the fracture strength of a stiffened sheet is examined using the Strip Yield Model of a crack. This model is relatively simple to apply and has contributed significantly to the fracture analysis of unstiffened structures and, to a more limited extent, to the analysis of stiffened structures. Following previous developments the MSD is represented by a discontinuous strip yield zone ahead of the main crack. The solution is extended in the present work to a crack in a stiffened sheet and results are determined for the crack tip opening displacement and the strip yield zone length for a crack in a typical MSD distribution. The model is used to compare the effect of MSD on the main crack for these structural variables. INTRODUCTION The Displacement Compatibility Method (DCM), has been used extensively (see citations in ref 1) for the analysis of cracked, reinforced sheets typical of those used in the aircraft industry. Applications of the DCM have proved both efficient and versatile for the determination of attachment forces and stress intensity factors in stiffened sheet structures. For high strength materials it is possible to use the principles of Linear Elastic Fracture Mechanics (LEFM) and to base the analysis on the Stress Intensity Factor of the crack. For medium and low strength materials where yielding at the crack tip may exceed the limits required for LEFM to apply it is necessary to use the principles of Non-linear Fracture Mechanics (NLFM). One method of doing this is to use a Strip Yield Zone (SYZ) model of the crack for which the fracture analysis is based on the Crack Transactions on Engineering Sciences vol 13, © 1996 WIT Press, www.witpress.com, ISSN 1743-3533 566 Localized Damage Tip Opening Displacement (CTOD) or Energy Release Rate of the crack. The SYZ model [2] has been used in the analysis of reinforced sheets structures [35]. This previous work was restricted the a single lead crack in the stiffened sheet. The model has also been extended to the analysis of multiple cracks [6] in which the interaction between the multiple cracks, such as occurs in MSD, was accounted for by using the displacement and stress field for the single crack together with the crack line Greens Function for a single crack in a Schwarz alternating process. In the present work the MSD is represented by introducing regions of zero traction into the strip yield zone between which are regions of uniform traction having a magnitude equal to the yield strength of the material. This representation of the MSD enables the single SYZ model to be directly entended to take account of the effect of multiple site damage by having the strip yield zone distributed discontinuously. Each gap in the yield zone tractions corresponds to the region of damage and each junction corresponds to the yielded ligament between the damage sites. A similar approach, based on a dislocation model of the MSD, has been used [7]. This model was used to analyze the effect of MSD on a lead crack in an unstiffened sheet and then create a modified single SYZ model for the analysis of stiffened sheets. In the present work the MSD is represented as a discontinuous distribution of tractions for both the unstiffened and stiffened sheet. THEORETICAL FORMULATION AND SOLUTION OF EQUATIONS The analysis is based on the complex variable technique due to Muskhelishvili [8] which states that the stress/displacement state within a multiply connected, two dimensional body subjected to in-plane loading may be completely specified in terms of two complex stress functions which can be written in series form. The system equations are formed by satisfying equilibrium of forces at, and compatibility of displacements between the attachment points, and by satisfying the strip yield crack condition that the stresses be bounded at the tip of the yield zone (Dugdale Condition). The system equations are solved for the unknown distribution of attachment forces and the unknown ratio of the sheet stress to the yield stress of the sheet material.The CTOD of the crack is determined from the attachment forces and the applied stress ratio for a specified distribution of MSD in the yield zone. CONFIGURATION STUDIED The configuration to be studied in the present work is shown in Fig. 1. It consists of an infinite sheet containing a lead crack of length 2a centered at the origin of the coordinates (x = 0,jy = 0). The lead crack has a series of of collinear cracks symmetrically located on either side of each tip which are joined by ligaments at the yield stress of the material the outer ones of which have strip yield zones at their tip. The region of MSD and the outer tip yield zones extend a distance s from the tip of the lead crack. The collinear cracks, which represent the MSD, are located under doubly riveted stiffeners with a stiffener across the Transactions on Engineering Sciences vol 13, © 1996 WIT Press, www.witpress.com, ISSN 1743-3533 Localized Damage 567 centre of the lead crack. The sheet is subjected to a uniform stress a perpendicular to the crack line. Fig. 1 Lead crack and Multiple Site Damage in a Uniformly Stressed Stiffened Sheet In general the sheet is reinforced by arbitrarily spaced stiffeners parallel to the yaxis. The stiffeners are attached to the sheet at discrete points symmetrically either side of the x-axis. The first attachment point is PQ from the x axis and all the other attachment points are a distance p apart . The attachment points are assumed to be represented by localised forces at the center of a rigid insert of diameter d. The sheet has a modulus of elasticity E, Poisson's ratio v and thickness t. The Young's modulus and area of each stiffener is E$ and Aj respectively. The effect of the in-plane and out of plane bending stiffness of each stiffener is assumed negligible compared to its axial stiffness, In the present work only a symmetrical distribution of two equal length MSD cracks, each side of the lead crack, is considered although the formulation allows for an arbitrary length and position of the MSD cracks It is also assumed that the center of the MSD cracks are symmetrically located across the center line of the attachments, Transactions on Engineering Sciences vol 13, © 1996 WIT Press, www.witpress.com, ISSN 1743-3533 568 Localized Damage The parameters used for modelling the stiffened sheet are given in Table 1 and represent a typical aircraft stiffened structure [3]. The stiffeners were attached at 15 points either side of the crackline along each rivet line. Parameter Sheet Modulus E Sheet Yield Strength