Showing papers on "Shear stress published in 1969"

Electrohydrodynamics: A Review of the Role of Interfacial Shear Stresses

Abstract: Electrohydrodynamics of fluids having uniform electrical properties, emphasizing shear effects for interfacially confined electromechanical coupling

Heat flow, stress, and rate of slip along the San Andreas Fault, California

Abstract: The absence of a heat flow anomaly greater than ∼0.3 µcal/cm2/sec associated with the San Andreas fault is used to estimate the upper limit for the steady state or initial shear stress. Under the assumption that the long-term rate of motion along the fault is 5 cm/yr and occurs primarily in the form of creep, this upper limit is about 100 bars. If the motion is primarily accomplished by faulting during large earthquakes and if the frictional stress is equal to the final stress as suggested by E. Orowan (1960), the upper limit is estimated to be about 200 bars. Without Orowan's assumption, the estimation of the upper limit is about 250 bars, based on earthquake energy-magnitude-moment relations. If the long-term rate of motion along the San Andreas fault is only ∼2 cm/yr, these results are increased to 250, 350, and 400 bars, respectively.

On the Coulomb-Mohr failure criterion

Abstract: Coulomb's criterion for the shear fracture of a brittle material is that total shearing resistance is the sum of the cohesive shear strength (independent of direction) and the product of the effective normal stress and the coefficient of internal friction (a constant independent of normal stress). Mohr generalized this criterion by extending it to a three-dimensional state of stress, and by allowing for a variable coefficient. The coefficients of internal and external (sliding) friction are not the same in general. Both tend to decrease with increasing normal stress, and their relative magnitudes may determine if failure occurs by new shear fracturing or by slip on pre-existing cohesionless surfaces like joints in rocks.

Neutron Starquakes and Pulsar Periods

Abstract: THE outer layers of neutron stars form a solid crust with a calculable rigidity (shear modulus) very soon after the stars are born. Subsequent changes in stellar shape from oblate toward spherical, as the neutron star angular velocity decreases, will induce stresses in the crust until the maximum shear strain which the solid can support is reached. Beyond this yield point there will be a sudden relaxation of the stress, and a very slight change in stellar shape and moment of inertia. The calculated accompanying jump in angular velocity is close to that which has been observed in a pulsar.

Anemoclinometer measurements of reynolds stress and heat transport in the atmospheric surface layer

Abstract: : A small, three-dimensional pressure-probe anemometer (IMFL anemoclinometer) was used to measure the three components of the wind vector, shear stress, and the ratio of the standard deviation of the vertical wind to the friction velocity as influenced by atmospheric stability. Horizontal wind and shear stress have been compared with independent wind profile and shear stress meter measurements. The anemometer was coupled with a fast thermometer for eddy correlation measurements of sensible heat flux and with a fast hygrometer for measurements of latent heat flux. The eddy correlation measurements of sensible and latent heat fluxes were compared with independent energy balance, wind profile, and sonic anemometer-thermometer measurements.

Electrohydrodynamic Charge Relaxation and Interfacial Perpendicular‐Field Instability

Abstract: The small‐amplitude motions of a plane interface between two fluids stressed by an initially perpendicular electric field are investigated. The fluids are modeled as Ohmic conductors and the convection of the surface charge caused by the dynamic interplay of interfacial electric shear stresses and the viscous stresses is highlighted. The influence of viscosity on instability growth rates in the zero‐shear stress limits of perfectly conducting and perfectly insulating interfaces is described and compared to cases involving electrical shear stresses. Detailed attention is given to the instability of an interface between fluids having electrical relaxation times long compared to times of interest. It is shown that, for many common liquids, even a slight amount of surface charge makes the interface unstable at a considerably lower voltage than would be expected from theories based on the dielectrophoretic limit of no interfacial free charge. Experiments, performed using high‐frequency ac stresses, gradually increased dc fields, and abruptly applied dc fields, support the theoretical model. In the general case, the electric Hartmann number is identified as an index to the dominance of the electric shear stresses over the viscous shear stresses in determining the interfacial convection of free charge.

Dislocation Dynamics and Steady Plastic Wave Profiles in 6061‐T6 Aluminum

Abstract: Under certain conditions, plastic wave profiles in 6061‐T6 aluminum may achieve a constant wave velocity and steady shape within a few millimeters from the impact surface in a plate‐impact experiment. The finite rise time of the steady plastic wave is assumed to be controlled by the motion of dislocations within the solid. The theory of steady‐propagating waves is presented and theoretically determined wave profiles are compared with those measured experimentally by means of laser interferometry. These studies provide information on dislocation velocity and multiplication under conditions of shock‐wave compression. In particular, if the mobile dislocation density is assumed to be a function of plastic strain alone, the dislocation velocity is found to be proportional to (τ−τ0)n, where τ is the applied shear stress, τ0 is a back stress, and n is a constant approximately equal to 2. Thus, it appears that a linear relationship between dislocation velocity and shear stress, which has been found to apply for strain rates less than 10−2 μsec−1 in aluminum, may not be sufficient to describe rate‐dependent behavior at strain rates greater than 10−2 μsec−1, which are achieved in shock‐wave compression.

Flip chip module with non-uniform connector joints

Abstract: The interconnecting joints between a semiconductor chip and a substrate are not uniform, but differ in shape or material The difference results in different abilities to withstand shear stress and increases the device lifetime A volume differential causes a stress resistance differential in the interconnection joints

Length Optimization for Constrained Viscoelastic Layer Damping

Abstract: Viscoelastic materials are used extensively to damp flexural vibrations of metallic structures; it has been known for some time that the energy dissipation due to shear strain in the viscoelastic layer can be increased by constraining it with a stiffer covering layer. In this paper, we will discuss a method for increasing this damping by cutting the constraining layer into appropriate lengths. The analysis for a single layer of this treatment is relatively straightforward. The damping can be increased still further by using several layers; in this case, the analysis is based upon effective complex elastic moduli of an equivalent homogeneous medium. One result found from this analysis is that, if the element length of the constraining layer is optimum, the damping depends primarily upon the stiffness of the constraining layer and the loss coefficient of the viscoelastic material, and only indirectly on the shear modulus of the viscoelastic layer. Experimental data is presented for comparison with the theoretical predictions.

The use of eigenfunction expansions in the general solution of three-dimensional crack problems

Abstract: Eigenfunction expansion technique to analyze three dimensional crack and wedge problems, emphasizing stress field near straight edged crack

Closure on vibration modulus of normally consolidated clay

Abstract: THE WRITERS ARE GRATEFUL TO WHITMAN, HOLT AND MURPHY, AND DOBRY AND POBLETE FOR DEMONSTRATING THE GOOD AGREEMENT BETWEEN VALUES OF THE SHEAR MODULUS CALCULATED IN THE PRESENTED EQUATION AND SHEAR WAVE VELOCITIES MEASURED IN THE FIELD BY GEOPHYSICAL METHODS AT TWO DIFFERENT SITES. TEST RESULTS SHOW THE EFFECT OF VOID RATIO, AMBIENT STRESS, STRESS HISTORY, FREQUENCY, AND STRAIN AMPLITUDE ON THE VIBRATION SHEAR MODULUS OF THESE UNDISTURBED SAMPLES. INDEX PROPERTIES IN THE CLASSIFICATION OF VARIOUS UNDISTURBED COHESIVE SOILS TESTED ARE PRESENTED IN A TABLE AND THEIR PARTICLE SIZE DISTRIBUTIONS SHOWN IN A FIGURE. THE VALUES OF VOID RATIO ARE PRESENTED IN A FIGURE. ANOTHER FIGURE PRESENTS THE EFFECT OF ISOTROPIC COMPONENTS OF STRESS ON UNDISTURBED SAMPLES. THE EFFECT OF OVERCONSOLIDATION RELATIONSHIPS ARE PRESENTED. WHITMAN, HOLT AND MURPHY HAVE PRESENTED A FIGURE SHOWING A CURVE BY WHICH THE MODULUS FOR HIGHER STRAIN AMPLITUDES MAY BE COMPUTED FROM THE MODULUS AT SMALL STRAIN AMPLITUDES. RESULTS ARE PRESENTED IN A FIGURE OF (1) COHESIVE SOIL AND (2) DRY SANDS WHICH WERE TESTED AT DIFFERENT FREQUENCIES AND NUMBERS OF CYCLES. DATA FOR BOTH HOLLOW AND SOLID CYLINDRICAL SPECIMENS SHOWED THE EFFECT OF THE VARIATION OF STRAIN WITHIN THE SPECIMEN TO BE SMALL. THIS IS ALSO TRUE FOR LARGE STRAIN AMPLITUDES PROVIDED THE MEASURED PARAMETERS ARE CORRELATED TO THE AVERAGE SHEAR STRAIN AMPLITUDE IN THE SPECIMEN. THE RESULTS FOR TWO SENSITIVE CLAYS ARE SHOWN IN A FIGURE. THE SPECIAL STRUCTURE OF HIGHLY SENSITIVE CLAYS APPEARS TO INCREASE THE MODULUS ABOVE THAT FOR LESS SENSITIVE SOILS WITH SIMILAR VOID RATIO AND STATE OF STRESS. REFERENCES: VIBRATION MODULUS OF NORMALLY CONSOLIDATED CLAY, BOBBY O. HARDIN, WILLIAM L. BLACK, ASCE PROCEEDINGS PAPER 5833, MARCH, 1968.

The stress at which dislocations are generated at a particle-matrix interface

Abstract: When a hydrostatic pressure is applied to a metal containing particles or inclusions of different elastic constant, the local shear stresses which develop can be large enough to cause the interface between the particle and the metal matrix to emit dislocations. We have measured the pressure (from which we calculate the local shear stresses) at which dislocations are first generated at SiO2 and Al2O3 particles in a copper matrix at room temperature. The critical pressure, and thus shear stress, depends on the particle size. The maximum shear stress at the particle surface was about G/100 for 2000 A diameter particles, rising to G/40 for 1000 A diameter particles, where G is the shear modulus of the metal matrix.

Effects of shear stress on the crystallization of linear polyethylene and polybutene‐1

Abstract: The effects of shear stress on the crystallization kinetics and morphology of linear polyethylene and polybutene-1 were studied with the aid of a specially designed apparatus. With this equipment, it was possible to heat a thin polymer sample between glass slides to a melt temperature, quench the sample to a crystallization temperature, and then deform the sample in shear by applying a constant load to one of the glass slides. During the deformation, the crystallization process was observed and photographed under a polarizing microscope. Also, the displacement of the glass slide was simultaneously recorded which made possible a determination of the shear strain as a function of time. The results demonstrate that two phenomena may occur in the initially supercooled polymer samples in response to the applied shear stress. In one case, the sample deformed until it fractured, generally exhibiting no evidene of crystallization; in the other, the sample deformed until an inflection point was reached after which the sample became rigid. This latter phenomenon was attributed to crystallization. At low shear stresses, the inflection point was associated with the growth of spherulites which simply became large enough to bridge the glass slides and prevent further deformation of the sample. This generally occurred prior to the completion of the radial growth of the lamellae. At high shear stresses, however, no evidence of crystallization was seen in the microscope until the inflection point was reached. At this point, birefringence was observed in the sample. The resulting structure generally could not be resolved in the microscope, thereby indicating very profuse nucleation. The results obtained clearly demonstrate that the application of a sufficiently high shear stress to an initially supercooled melt has a substantial effect on the rates of crystallization of both polyethylene and polybutene-1. This was shown most dramatically at temperatures close to the melting point, e.g., both polyethylene at 130°C and polybutene-1 at 113°C, which require over 104 sec to crystallize under quiescent conditions, crystallized at approximately 0.05 seconds. The application of a shear stress to a polymer melt is envisaged as resulting in molecular orientation. In accord with the theories of Flory, and Krigbaum and Roe, the associated decrease in entropy of the melt may be considered to increase the supercooling. Under high stresses at which large increases in supercooling result, crystallization occurs more rapidy at the high temperatures and with polymers of lower molecular weight. At low shear stresses, the influence of temperature and molecular weight on the crystallization kinetics is essentially the same as that obseved under quiescent conditions. Observations through the microscope have shown that the application of a shear stress to a polymer melt leads to large increases in the number of crystalline structures formed and to the formation of oriented morphologies. This latter phenomenon arises due to nucleation lines formed by impurities and spherulites in the deforming melt. The impurities and spherulites apparently cause a disturbance which is thought to result in a local increase in stress of the melt and, hence, a local increase in supercooling. Lamellae then nucleate on these lines and grow out radially.

The laminar boundary layer on a moving continuous flat sheet immersed in a non-Newtonian fluid

Abstract: The laminar boundary layers on a moving continuous flat surface in non-Newtonian fluids characterized by the power law model are investigated using exact and approximate methods. Both pseudoplastic and dilatant fluids are considered. Numerical solutions of the boundary-layer equations are obtained for values of the parameter n in the power law model ranging from 0.1 to 2.0. An integral solution of the momentum equation, which can be used to obtain values of the dimensionless shearing stress that are in good agreement with the exact values, is developed. An integral solution to the energy equation is also presented.

Mobility of Dislocations in Aluminum

Abstract: The velocities of individual dislocations of edge and mixed types in pure aluminum single crystals were determined as a function of applied‐resolved shear stress and temperature. The dislocation velocities were determined from measurements of the displacements of individual dislocations produced by stress pulses of known duration. The Berg‐Barrett x‐ray technique was employed to observe the dislocations, and stress pulses of 15 to 108 μsec duration were applied by propagating torsional waves along the axes of [111]‐oriented cylindrical crystals. Resolved shear stresses up to 16×10^6 dynes∕cm^2 were applied at temperatures ranging from −150° to +70°C, and dislocation velocities were found to vary from 10 to 2800 cm∕sec over these ranges of stress and temperature. The experimental conditions were such that the dislocation velocities were not significantly influenced by impurities, dislocation curvature, dislocation‐dislocation interactions, or long‐range internal stress fields in the crystals. The velocity of dislocations is found to be linearly proportional to the applied‐resolved shear stress, and to decrease with increasing temperature. Qualitative comparison of these results with existing theories leads to the conclusion that the mobility of individual dislocations in pure aluminum is governed by dislocation‐phonon interactions. The phonon‐viscosity theory of dislocation mobility can be brought into agreement with the experimental results by reasonable choices of the values of certain constants appearing in the theory.

Volume change characteristics of unsaturated clay

Abstract: Compression tests under controlled effective stress paths show the stress path independence of volumetric strain and degree of saturation. Stress path dependency appears to be caused by a reversal in the direction of saturation. The swelling process does not in itself appear to introduce an important path dependency. The collapse mechanism is controlled by a potentially unstable structure, a high applied stress and a high suction pressure. The absence of one of these three factors removes the possibility of significant collapse. The effect of molding water content and compaction method on the structure of compacted clay is illustrated by the different compression behavior of clays compacted dry and wet of optimum. The compression behavior is treated best in terms of the separate components of applied stress and suction pressure, and for one-dimensional compression, the stress-strain relationship for a clay can be stated in a simple form.

Shear Strength of Reinforced Concrete Beams

Abstract: The stress distribution at failure and the failure modes of reinforced concrete beams with and without web reinforcement failing by shear-compression have been investigated Stress redistribution which takes place at the diagonal tension cracking load is caused by internal local rotation, which increases the width of the diagonal tension cracks The crack width is proportional to the distance from the center of rotation at the apex of the diagonal tension crack The ultimate strength of beams failing by shear-compression is dependent on the location of the diagonal tension crack within the compression zone, and the shear span ratio The diagonal tension crack is located at the center of the compression zone

Dynamic Interaction of a Shear Wall with the Soil

Abstract: An analysis is presented of the interaction between a shear wall, placed on a rigid foundation, and soil when the soil is subjected to a plane shear wave. Due to the particular symmetry of the model adopted an exact closed-form solution is obtained for the steady state response. The base displacements and base shear forces are compared with the corresponding values obtained neglecting the interaction. It is shown that the base displacements are zero for the fixed-base natural frequencies of the shear wall.

Finite element analysis of inelastic structures.

Abstract: Differential stress-strain relationships are used to generate a system of simultaneous firstorder differential force-displacement equations which are integrated numerically to obtain the stresses, strains, and displacements in inelastic structures. For the biaxially stressed element, the concept of isotropic hardening and a generalized stress are used to evaluate an effective modulus and Poisson's ratio, which vary continuously from their initial values during elastic straining action to their asymptotic values during intense plastic straining action. The surface of plasticity for this element closely approximates the von Mises surface when the generalized stress is set equal to the von Mises stress and the strain distribution is essentially identical to that obtained by the Prandtl-Reuss incremental flow theory. The analysis of the MIT shear lag structure is presented to demonstrate the applicability of the method to systems of practical size and interest. Nomenclature A = equilibrium matrix B = compatibility matrix C = stress-strain matrix C = differential stress matrix E = Young's modulus Et = tangent modulus Es = secant modulus K — stiffness matrix K = differential stiffness matrix P = applied load parameter u = element nodal displacements X = element nodal forces X = load constant n = Poisson's ratio fjLt = tangent Poisson's. ratio Us = secant Poisson's ratio e = strain a- = normal stress

Mechanics of Second Order Faults and Tension Gashes

Abstract: The origin of en echelon second order shear fractures and tension gashes associated with first order, or primary, faults is examined analytically and experimentally. It is postulated that en echelon second order structures form under the influence of a stress mechanism similar to the one occurring in the direct shear test. The direct shear or modified direct shear state of stress could develop at certain points along a forming primary fault as a result of a local reduction in the normal stress acting on planes perpendicular to the displacement direction. It is argued that in most en echelon arrays the orientation of the individual fractures reflects the existence of a local state of stress, and cannot directly be correlated with the regional (primary) stress field. The zone in which they occur, however, may represent planes of high effective shear stress within the regional framework. The direct shear model (full relief of transverse normal stress) offers a stress mechanism which can explain the origin of not only en echelon tension gashes but also second order faults. For a given set of strength parameters, the type of en echelon fractures that will develop depends on the normal stress acting in the primary fault plane. In general, tension fractures form at low normal stress, shear fractures at intermediate values of normal stress, and at high normal stress a crush or shear zone is produced. If the state of stress is one of modified direct shear (only partial relief of transverse normal stress), the development of second order faults is favored.

Intrinsic Errors in Pressure‐Hole Measurements

Abstract: A convenient way of measuring normal thrusts on fluid‐immersed surfaces is by use of a pressure gauge attached to a hole in the surface. With viscoelastic fluids exhibiting normal stress effects, it is shown that a systematic error exists, independent of hole size, but dependent on wall shear stress. Experiments were made in an open channel with various holes from 132 in. to 14 in. diameter, and also with an 18 in. wide slot. Errors were small with 30P silicone fluid, but with two viscoelastic solutions errors were always negative and of the order of 25% of the first normal stress difference. No significant difference has been seen yet between sharp‐edged holes of different sizes or between holes and slots. A theoretical treatment for plane creeping flow over a deep slot predicts that the error is negative, independent of slot width, and 25% of the first normal stress difference. Some implications for normal stress measurements are considered.

Stress Concentrations from Single-Filament Failures in Composite Materials:

Abstract: The solution of the two-dimensional, elastic, multiple-filament-failure stress concentration problem led to the treatment of three-dimensional, elastic failure models and a two-dimensional, plastic...

The measurement of skin friction in turbulent boundary layers with adverse pressure gradients

Abstract: This paper describes a floating-element skin friction meter which has been designed for use in adverse pressure gradients. The effects of secondary forces on the element, which arise from the pressure gradient, are examined in some detail. The limitations of various methods of measuring wall shear stress are discussed and the results from the floating element device are compared with measurements taken in a two-dimensional boundary layer using Preston tubes and velocity profiles. As it is planned to use the instrument later for direct measurements of the shear stress in three-dimensional boundary layers, the relevance of the instrument to this situation is also discussed.

On wind and shear stress profiles above a change in surface roughness

Abstract: The problem of determining the distribution of velocity and shear stress in the flow above a surface with an abrupt change in roughness is considered by using the ‘mixing-length’ theory to relate the shear stress to the velocity profile and solving the resulting system of partial differential equations numerically. The results are compared with those obtained by Panofsky and Townsend (1964) and Taylor (1967), by assuming special forms for the velocity or shear stress profiles.

Flow of Polymer Melts in Extruders. Part I. The Effect of Transverse Flow and of a Superposed Steady Temperature Profile

Abstract: Steady flow in the metering section of relatively narrow channel extruders can be regarded as a special case of curvilineal viscometric flow (as defined by Coleman, Markovitz, and Noll). It is shown that under these conditions the behavior of simple fluids can be adequately described from knowledge of a single shear stress function. To specify this function an extended form of the power‐law relationship is used, as it agrees well with viscometric measurements on polymer melts over a range of shear rates. The equations of motion and energy are solved taking into account the effect of transverse flow in the channel and of a superposed steady temperature profile. Results of the numerical computations are presented in terms of dimensionless parameters, and comparison is made with experimental results. The marked effect on non‐Newtonian fluid behavior on extruder output at low back pressures and on the shape of the screw characteristics is emphasized. The importance of temperature effects is measured by the ma...

The effect of pressure gradient on the law of the wall in turbulent flow

Abstract: The effect of a streamwise pressure gradient on the velocity profile in the viscous sublayer of a turbulent flow along a smooth wall in two-dimensional flow is estimated. In the analysis, a similarity argument is used and the necessary empirical information obtained from a constant pressure flow. An allowance is made for the departure from the wall value of the gradient of total shear stress normal to the wall. The results of analysis were used to generate new additive constants for use with Townsend's modified law of the wall velocity profile and subsequently Townsend's profile is found to be in good agreement with the measured velocity profiles in an adverse pressure gradient.