Showing papers on "Shear stress published in 1978"

Friction of Rocks

Abstract: Experimental results in the published literature show that at low normal stress the shear stress required to slide one rock over another varies widely between experiments. This is because at low stress rock friction is strongly dependent on surface roughness. At high normal stress that effect is diminished and the friction is nearly independent of rock type. If the sliding surfaces are separated by gouge composed of Montmorillonite or vermiculite the friction can be very low.

Description of the non-linear shear behaviour of a low density polyethylene melt by means of an experimentally determined strain dependent memory function

Abstract: The applicability of a single integral constitutive equation with strain dependent memory function for the description of the nonlinear shear behaviour of a LDPE melt is examined. The generalized memory function is expressed as a product of Lodge's rubberlikeliquid memory function $$\mathop \mu \limits^ \circ (t - t\prime )$$ and a damping function h(γt, t′). $$\mathop \mu \limits^ \circ $$ characterizes the time dependence of the linear viscoelastic behaviour and is determined by measurements of the frequency dependence of the complex shear modulus. The damping function describes the nonlinearity of the shear behaviour and can directly be determined by measurements of the shear relaxation modulus. From the temperature invariance of the damping function it follows that also in the nonlinear range a variation of temperature only corresponds to a shift in time scale which can be described by the shift factora T (T). By means of the experimentally determined memory function the shear viscosity and the primary normal stress coefficient as functions of shear rate and temperature can be predicted. The time dependence of the shear stress and of the primary normal stress difference in stressing tests and the relaxation behaviour is described correctly.

Micromechanisms of flow and fracture, and their relevance to the rheology of the upper mantle

Abstract: Crystalline solids respond to stress by deforming elastically and plastically, and by fracturing. The dominant response of a given material depends on the magnitude of the shear stress (0 s ), on the temperature (T) and on the time (t) of its application. This is because a number of alternative mechanisms exist which permit the solid to flow, and its fracture, too, occurs by one of a number of competing mechanisms. Their rates depend on 0 8 , T and t: it is the fastest one which appears as dominant. In geophysical problems, pressure appears as an additional variable. At pressures corresponding to depths of a few kilometres below the surface of the Earth, the mechanisms of fracture are the most affected; but at depths of a few hundred kilometres, plasticity, too, is influenced in important ways. This paper outlines the mechanisms of flow and fracture which appear to be relevant in the deformation of materials of interest to the geophysicist, and the way pressure affects them. The results are illustrated and their shortcomings emphasized by using them to calculate the mechanisms of flow and fracture to be expected in the upper mantle of the Earth.

Dynamics of rod-like macromolecules in concentrated solution. Part 2

Abstract: As a continuation of a previous paper, the rheological properties of a concentrated solution of rod-like macromolecules are discussed. A procedure for calculating the stress tensor for a given flow history is presented and, as a special case, simple steady shear flow is studied in detail. Some interesting feature of the results are: (i) the steady state viscosity η(0) at zero shear rate and the first and second normal stress coefficients Ψ1(0) and Ψ2(0) all depend very strongly on molecular weight M and mass concentration ρ, with η(0)∝ρ3M6 and Ψ1(0), Ψ2(0)∝ρ5M13; (ii)Ψ2(g) is negative and about –2/7 of Ψ1(g) where g is the velocity gradient; (iii) the shear stress shows an extremum as a function of shear rate, indicating an instability of flow at certain shear rate. As a byproduct of the theory, a stress-optical law is predicted.

Shear in beam - column joints in seismic design of steel frames

Abstract: This paper discusses the importance of joint shear in the response of frame structures to severe earthquakes. Presently used AISC design criteria for joint shear are reviewed in the light of limited experimental evidence. The effects of high shear in joints on the strength, stiffness, and energy-dissipation characteristics of frames are discussed. The most important conclusions can be briefly summarized: Joints usually are very ductile elements capable of undergoing severe inelastic strain reversal without a decrease in strength. The shear force defined by the AISC design equation for combined gravity and lateral loads usually causes some inelastic deformation in joints. This is reduced when the allowable shear stress is modified by the factor alpha, which accounts for the effect of the axial force in the column on the yield stress in shear. Solutions for the ulimate shear strength, associated with controlled inelastic distortions, are given, for joints with unreinforced and reinforced webs, respectively. When joints are designed according to allowable stress criteria, inelastic deformations may be concentrated primarily in the joints and to a lesser degree in plastic hinge regions of beams and columns. Maximum strength and stiffness of frames is attained when all joints are designed for the maximum shear force that can be developed based on the strength capacity of the members framing into the joint. The need for this design criterion has not been fully established, although it is widely used in areas of high seismicity. If this criterion is used, the joints should be permitted to participate in energy dissipation through inelastic deformations. Joint distortions contribute significantly to the elastic story drift in frames. Equations are given which permit an estimate of the effect of these distortions on the lateral deflections.

Formation of shear bands in sand bodies as a bifurcation problem

Abstract: The paper reports on the results of theoretical and experimental investigations on the spontaneous formation of shear bands in sand bodies. The phenomenon is considered as a bifurcation problem. Consequently, material response and configuration-dependent loading determine the bifurcation mode. Both Coulomb's and Roscoe's solutions of inclination of the shear band can be correct theoretically and experimentally. The first one holds for non-rotating stress axes, the second one for co-rotating stress and strain increment axes during failure. Values in between can occur if the rotation of principal stress axes is not equal to one of these limits. If Coulomb's inclination of shear band occurs, there is a thin deforming material layer separating rigid bodies. Inside the shear band non-coaxiality of strain increment and stress holds from the beginning. If Roscoe's inclination of shear band occurs, it is separating two deforming bodies. Inside the shear band strain increment and stress are coaxial at peak.

Bond Thickness Effects upon Stresses in Single-Lap Adhesive Joints

Abstract: Results of an analytical investigation on the influence of bond thickness upon the stress distribution in singlelap adhesive joints are presented. The present work extends the basic approach for bonded joints, orginally introduced by Goland and Reissner, through use of a more complete shear-strain/displacement equation for the adhesive layer. This refinement was not found to be included in any of the numerous analytical investigations reviewed. As a result of the approach employed, the present work uncovers several interesting phenomena without adding any significant complication to the analysis. Besides modifying some coefficients in the shear stress equations, completely new terms in the differential equation and boundary conditions for bond peel stress are obtained. Sn addition, a variation of shear stress through the bond thickness, no matter how thin it may be, is analytically predicted only by the present theory. This through-the-bond-thickness variation of shear stress identifies two antisymmetrical adherend-bond interface points at which the shear stresses are highest. The growth of joint failures originating from these points agrees with results obtained from actual experiments.

Mantle flow pressure and the angle of subduction: Non-Newtonian corner flows

Abstract: Corner flows of Newtonian and non-Newtonian fluids are used to model the flow in a subduction zone which is viscously driven by the motions of the converging plates and the descending slab. The pressures induced by the flow tend to lift the slab up beneath the overriding plate thereby offsetting the tendency of gravity to align the slab with the vertical. The low angles of subduction observed in Peru and Central Chile may be the result of strong dynamic pressures forcing the slab up against the overriding plate. Viscous coupling between the overriding plate and the downgoing slab is essential if the nonvertical dips of slabs are a consequence of the balance between gravitational and pressure torques. For a Newtonian mantle, shear stresses and pressures on the top of the slab are comparable. If the mantle is non-Newtonian, however, the pressures greatly exceed the shear stresses, for most acute dip angles. Thus frictional forces on the top and bottom surfaces of slabs are less important in resisting slab descent into a non-Newtonian mantle than they are in resisting penetration into a Newtonian mantle.

The effect of short regions of high surface curvature on turbulent boundary layers.

Abstract: Measurements, including one-point double, triple or quadruple mean products of velocity fluctuations, have been made in low-speed turbulent, boundary layers on flat surfaces downstream of concave or convex bends with turning angles of 20 or 30 degrees, the length of the curved region being at most 6 times the boundary-layer thickness at entry. These short bends approximate to ‘impulses’ of curvature, and the object of the work was to investigate the impulse response of the boundary layer, essentially the decay of structural changes downstream of the bends. The work can be regarded as a sequel, with much more detailed measurements, to the study by So & Mellor (1972, 1973, 1975) who investigated the response to step increases of curvature: turbulent boundary layers being nonlinear systems, responses to several kinds of curvature history are needed to assemble an adequate description of the flow. The most striking feature of the ‘impulse’ response is that the decay of the high turbulent intensity found at exit from the concave bends is not monotonic; the Reynolds stresses in the outer layer collapse to well below the level at entry, and are still falling slowly at the end of the test rig although in principle they must recover eventually. On the convex (stabilized) side the flow recovers, monotonically in the main, from a low level of turbulent intensity at the exit. The pronounced second-order response on the concave side can be explained qualitatively by interaction between the shear stress and the mean shear and is not peculiar to curved flows, but in the present cases the response is complicated by large changes in the dimensionless structure parameters related to double or triple mean products of velocity fluctuations. Strong spanwise variations, due presumably to longitudinal vortices, further complicate the flow in the concave bends, and decay only very slowly downstream.

Line Crack Subject to Shear.

Abstract: Field equations of nonlocal elasticity are solved to determine the state of stress in the neighborhood of a line crack in an elastic plate subject to a uniform shear at the surface of the crack tip. A fracture criterion based on the maximum shear stress gives the critical value of the applied shear for which the crack becomes unstable. Cohesive stress necessary to break the atomic bonds is calculated for brittle materials.

Stress and temperature in subduction shear zones: Tonga and Mariana

Abstract: Summary. Because there is secondary sea-floor spreading in the Tonga and Mariana subduction systems, the island arcs are separate plates. Horizontal forces on the two sides of the arc must balance, and the maximum force on the back-arc side can be calculated from a lithostatic ridge model. This, in combination with gravity data, allows calculation of the average shear stress in the top 100 km of the subduction shear zone. Stress in Tonga is 220±100 bar, and in the Mariana it is 165±75 bar. These low stresses are probably made possible by a fluid pore pressure almost equal to the least compressive stress. Knowledge of stress allows approximate calculation of temperature in the shear zone by integration of a single differential equation. These temperatures are too low to activate most dehydration reactions in the subducted crust. As it approaches the volcanic line, this crust is at 150–350°C in Tonga and 150–300°C in the Mariana. Shear melting of the crust is ruled out, and conductive melting of the slab by contact with the asthenosphere meets with geochemical objections. Magmas in these systems are probably produced by partial melting of asthenosphere, triggered by a sudden release of water from the slab.

Studies on multilayer film coextrusion II. Interfacial instability in flat film coextrusion

Abstract: An experimental study was carried out to investigate the phenomenon of interfacial instability in multilayer flat-film coextrusion. For the study, a sheet-forming die with a feed block was used to coextrude three-and five-layer flat films. Polymers coextruded were: (a) low-density polyethylene with polystyrene, and (b) high-density polyethylene with polystyrene. It was observed that, for a given polymer system, there is a critical value of wall shear stress at which an irregular (i.e., unstable) interface between the layers sets in, giving rise to a pattern similar to that usually found in a wood panel. Once the instability sets in, the severity of interfacial instability is found to depend on both the total volumetric flow rate (hence wall shear stress) of the combined streams and the ratio of the individual layer thicknesses. An attempt is made to correlate the critical conditions for the onset of interfacial instability in terms of the layer thickness ratio, and the viscosity and elasticity ratios of the two polymers being coextruded.

Tank Tread Motion of Red Cell Membranes in Viscometric Flow: Behavior of Intracellular and Extracellular Markers (with Film)

Abstract: With a cone and plate ‘rheoscope’, red cell suspensions can be observed while subjected to shear. Interference contrast optics and high speed cinematography allow resolution of details of deformation in native, unstained red blood cells (RBC) with an optical resolution of 0.3 μm and a time resolution of 2 ms. Movement of membrane and cytoplasm of RBCs is monitored by various markers. At shear rates above 500/s, red cells in whole blood (Hct > 40%) show elongation parallel to flow direction, whereas single red cells suspended in plasma (Hct < 5%) take irregular polyhedral forms and tumble in a shear flow at the same shear rate. Single cells suspended in viscous solutions (e.g. Dextran) under shear are deformed to form flat ellipsoids. Their elongation increases asymptotically towards a maximum with increasing shear stress. Ellipsoidally deformed RBCs assume a stationary orientation in the shear field, the long axis lying in a plane through the center of the cell containing the flow direction and perpendicular to the plate of the rheoscope. The angle between the long axis and the flow direction is zero only for very small and very large elongations. The membrane shows tank tread motion, the frequency of which increases linearly with the shear rate. Shear flow is transmitted from the continuous phase into the cytoplasm of the cell and can be observed directly by cytoplasmic markers. The shear rate within the cytoplasm is approximately constant. Assuming Newtonian behavior of both the continuous phase and the intracellular hemoglobin solution, the calculated shear stresses within the cell are lower by a factor of 4 than those in the continuous phase. Moderate stomatocytes and echinocytes (I and II) are also deformed to form stationary ellipsoids, irrespective of their preparation by different agents. The shear stresses required for their elongation are of the same order of magnitude as those required for discocyte elongation. Fragmentation of RBCs in shear flow and an altered appearance of the membrane after its plastic deformation in excessive shear could be observed.

The effect of anisotropy on the creep of polycrystalline ice

Abstract: Quantitative effects of crystallographic orientation fabrics are incorporated into the flow law for isotropic polycrystalline ice by the introduction of an enhancement factor applied to the isotropic fluidity. An aggregate is viewed to a first approximation as a collection of grains deforming independently by basal glide. The influence of preferred orientations on the mean intragranular rate of strain is treated in terms of a redistribution of the magnitude and orientation of resolved basal shear stress. A quantitative measure of this effect on the fluidity of the aggregate is provided through the development of a geometric tensor and a stress configuration parameter. Intergranular interference is then considered as a dissipative process modifying the fluidity of the aggregate. Empirical justification for the model at low octahedral shear stresses is provided by several laboratory creep tests on naturally anisotropic bore-hole specimens under both in situ and anomalous stress situations. Predicted enhancement factors ranged from approximately 0.2 to 2.8 and agree well with measured values. The tests were carried out in uniaxial compression and simple shear.

Nonlinear shear creep and constrained elastic recovery of a LDPE melt

Abstract: Shear creep and constrained elastic recovery experiments on a well characterized low-density polyethylene melt are reported. The temperature dependence of the shear strain and the primary normal stress difference is discussed in detail. Comparison is made with predictions of a strain-dependent single integral constitutive equation, which has already been successfully used for the same polymer melt to describe the stress growth after sudden imposition of a constant shear rate flow and stress relaxation after cessation of steady shear flow. It should be emphasized that this constitutive equation contains no adjustable parameters. The linear-viscoelastic part of the memory function is related to the linear-viscoelastic relaxation spectrum, while the nonlinear, strain-dependent part was determined from rapid-strain experiments. In the case of a prescribed shear stress history the resulting integral equation cannot be solved by closed integration but has to be inverted by numerical methods. Agreement between theoretical predictions and experimental data is rather encouraging for shear strain and primary normal stress difference during creep and retardation tests. Within experimental error, the strain and shear rate dependence of the recoverable portion of the total strain can be correctly predicted.

Platelet lysis and aggregation in shear fields.

Abstract: A rotational viscometer was used to study the effects of shear stress on platelets in human platelet-rich plasma (PRP). For 5-min exposure times, shear stresses above 160 dynes/cm2 induced platelet lysis (as determined by release of platelet lactic dehydrogenase). For 30-s exposure times, shear stresses greater than 600 dynes/cm2 were required to induce platelet lysis. The platelet counts of sheared PRP were decreased to as low as one-fifth the original count due largely to shear-induced aggregation. The count is a minimum at intermediate stress levels (200-400 dynes/cm2). Higher stresses induce disaggregation as well as lysis. The diminution in the counts was partially reversed in 2 h incubation after cessation of shearing. Experiments were carried out with three different viscometer configurations so that the shear stress and the solid surface area access could be varied independently. Surface access was not a significant variable in the conditions of the experiments. Thus aggregation and lysis may be induced by stress effects alone as well as by solid surface effects. The results also show that the response of platelets to shear stress is strongly dependent on exposure time. Platelets are much less resistant to shear stress than red cells for relatively long exposure times. However, the converse is true for very short exposure times.

Velocity characteristics of the flow in the near wake of a disk

Abstract: Measurements of the velocity characteristics of near-wake flows were obtained with a direction-sensitive laser-Doppler anemometer The wakes were formed downstream of central disks of diameters 8·9, 12·5 and 14·2 mm which were located on the centreline of a 20·0 mm jet Detailed measurements were obtained with initial annular-jet velocities of from 9·4 to 39·5 m/s and include values of the axial and radial components of the mean velocity, the three normal stresses and the shear stress Probability density distributions and energy spectra were also measuredThe results show, for example, that the curvature of the annular jet increases with disk diameter and that the ratios of the maximum positive and negative centre-line velocities to the exit velocity increase with decreasing disk diameter and are essentially independent of the initial velocity The turbulent field is substantially anisotropic with a minimum turbulence intensity of around 30% in the recirculation region; the locations of zero shear stress and zero mean velocity gradient are not coincident The measured spectra reveal predominant frequencies in a small region of the outer-shear layer and in the vicinity of the jet exit; these discrete frequencies did not propagate downstream nor into the recirculation region

Influence of transverse shear on an axial crack in a cylindrical shell

Abstract: An axial crack in a cylindrical shell is investigated by use of a 10th order shell theory, which accounts for transverse shear deformations as well as a special kind of orthotropy. The symmetric problem is formulated in terms of two coupled singular integral equations, which are solved numerically. The asymptotic membrane and bending stress fields ahead of the crack are found to be self similar. Stress intensity factors are given as a function of the shell parameter for various values of the ratio shell radius to shell thickness. Considerable differences from 8th order shell theory results are found for the bending stresses, while the membrane stresses of the 8th order theory seems to be a lower limit reached for very thin shells.