Local Stress Variations Research Articles

Decay rate of Saint-Venant end effects for multilayered orthotropic strips

Saint-Venant decay rate of end effects is investigated for generally laminated orthotropic strips under self-equilibrated end loads. The problem is governed by a fourth-order partial differential equation for the Airy stress function with discontinuous coefficients at the layer interfaces, where displacements and traction continuities are imposed. The solution is found in the form of product of an exponentially decaying function along the strip and an unknown function defined over its total height. External face and interface conditions are used to obtain the characteristic equation for the eigenvalues governing the decay rate of end effects along the strip. For orthotropic and strongly orthotropic sandwich strips the transcendental eigenvalue equation is explicitly given. The case of laminated strips with periodic layout is finally considered. Making use of the homogenization method, both effective elastic constants and expressions for the local stress variation at the layer level are obtained. Numerical calculations confirm that the eigenvalues of the homogenized material are the asymptotic values of those of periodically laminated strips when the number of layers increases. Moreover, homogenization method is shown to be very powerful also in the calculation of local stress distributions.

Residual strain effects on the stress field in a thick wall finite element model of the human carotid bifurcation

A three-dimensional finite element model of the carotid artery bifurcation was constructed in order to determine the stress field and assess the modification of the stress field when residual strain is taken into account. Residual strain in the carotid bifurcation was characterized by experimental observations. According to these observations, a geometrical model of the carotid artery was constructed to exhibit a state free of strain. Appropriate boundary conditions were applied to yield the correct geometry in the unloaded state, and physiological levels of pressure and axial stretching were applied. The model took into account the varying thickness of the arterial wall along the bifurcation. For modeling purposes, the material was considered to be hyperelastic, incompressible, homogenous and isotropic. For comparison, a similar model of the carotid artery which does not include the effects of residual strain was also created. The results demonstrate that in the model of the carotid artery bifurcation with residual strain, the distribution of maximum principal stress along the inner wall and the circumferential stress throughout the wall is much more uniform than in the model without residual strain. The ratio between the stress at the inner and the outer walls is highest at the lateral wall of the carotid sinus; this is the same location known to be a site of low and oscillatory fluid wall shear stress, and the principal location of early intimal thickening. These results suggest that the localization of atherosclerosis in the carotid artery may be due to local variations in both fluid wall shear stress and solid wall stress.

Experimental validation of mechanical stress models by micro-Raman spectroscopy

It is shown that micro-Raman spectroscopy offers a unique tool for the validation of stress models for microelectronics devices. Starting from an analytical or numerical model that describes the variation of local stress in a device, the corresponding Raman shift is calculated and compared with the data. In this way feed-back is given to the model. This technique is demonstrated for stripes (Si3N4, COSi2, W) on a Si substrate, but can be applied to any device where Raman data can be obtained.

MHD MIXED CONVECTION FROM A HORIZONTAL CIRCULAR CYLINDER

This work investigates analytically the effect of a radial magnetic field on the flow and heat transfer characteristics of mixed convection from a horizontal circular cylinder. Variable wall temperature is assumed at the cylinder surface. Two sets of transformations are used, one for forced-convection-dominated flow and the other for buoyancy-convection-dominated flow. The results are obtained numerically using the local nonsimilarity method and the coordinate perturbation method. The variation of local wall shear stress and local heat transfer along the circumference up to the point of separation and the velocity and temperature profiles in the boundary layer are obtained for varying values of the magnetic parameter (Ha2/Re) and the buoyancy parameter (Cr/Re2), which covers the entire regime of mixed convection from the pure forced convection to the pure free convection. It is found that the presence as well as the increase in the magnetic field leads to a decrease in the velocity field, local wall shear stress, and local Nusslet number and a rise in the values of temperature in the flow field.

Hardness-stress-strain correlation in aluminium—A simpler alternative to visioplasticity in metal forming

Local stress and strain variations in the deformation zone can be ascertained by measuring hardness. Hardness is correlated with strain and stress. The expressions discussed later are useful in determining the local variations in stress and strain from hardness measurement. It is a simple method compared to visioplasticity. One can estimate the forces required for a forming process. It helps in the choice of equipment, design of tooling and selection of lubricant for the particular process.

Some engineering and mathematical aspects on the homogenization method

Effective properties and local stress variations of elastic fiber composites are studied by means of the homogenization method. Two different methods, “the displacement method” and “the force method”, for solving the so called cell problem are derived, applied and compared. Numerical results for three different types of representative volume elements are presented. We also calculate the effective moduli of a unidirectional fiber composite for different volume fractions of fibers. The numerical results are discussed and compared with the Hashin-Shtrikman bounds.

Stress transfer in shear deformable discontinuous composites

It is well known that the shear lag theory is not to provide sufficiently accurate strengthening predictions when the fiber aspect ratio is small. This is due to its neglect of stress transfer across the fiber ends and the stress concentrations that exist in the matrix regions near the fiber ends. In this paper, a new approach to investigate stress transfer mechanisms in shear deformable discontinuous composites is proposed to overcome the shortcoming of shear lag theory. The modification scheme is based on the replacement of the matrix between fiber ends with the fictitious fiber to maintain the compatibility of displacement and traction. Thus, the proposed model takes fiber end effects into account and results in fully closed form solutions. It was found that the proposed model gives a good agreement with finite element results and has the capability to correctly predict the values of interfacial shear stresses and local stress variations in the small fiber aspect ratio regime.

Three patterns of distribution characterize the organization of endothelial microfilaments at aortic flow dividers

Since actin microfilaments are essential in the maintenance of endothelial integrity and in the repair of injured endothelium, we have carried out a detailed study of the distribution of microfilaments in the immediate vicinity of aortic branches. Branches are of major interest because there is a predilection for atherosclerotic lesions near branch ostia. We made an extensive, systematic examination of branches of the aorta and iliac arteries using in situ staining of perfusion-fixed arteries. Microfilaments were localized using rhodamine phalloidin. Three patterns of staining were observed. Some endothelial cells showed prominent central stress fibers. Others had few central stress fibers but prominent peripheral fibers. Still others showed an intermediate pattern with some central and some peripheral fibers present. At small branch sites, the lip of the divider was more blunt, and there were more cells with peripheral actin. At large branches, cells with peripheral actin were confined mainly to the lip, while there were many more cells with prominent central fibers. We also found that major differences can occur over very small distances, so adjacent cells may have strikingly different patterns of microfilament distribution. These patterns appear to reflect the geometry of the flow divider and local variations in hemodynamic shear stress. The differences in microfilament distribution may reflect differences in endothelial functions which are essential in maintaining endothelial integrity.

The application of neutron diffraction to stress mapping around a blind-hole defect in stressed pipeline steel

Neutron diffraction was used to map the local stress variation surrounding a 13 mm diameter blind-hole defect in a section of pipeline subjected to an applied bending stress. Comparison was made between the experimentally measured results and local stress predictions based on a two-dimensional analytical model as well as on three-dimensional finite element calculations. The two-dimensional analytical model proved to be unsatisfactory, predicting very large local stress variations at the defect edge which were not observed experimentally. Conversely, the three-dimensional model reflected all of the significant trends observed experimentally, although predicted stress levels were lower than the measured values due to limitations with the finite element package.

Geometry and kinematics of dunes during steady and unsteady flows in the Calamus River, Nebraska, USA

ABSTRACTThe geometry and kinematics of river dunes were studied in a reach of the Calamus River, Nebraska. During day‐long surveys, dune height, length, steepness, migration rate, creation and destruction were measured concurrently with bedload transport rate, flow depth, flow velocity and bed shear stress. Within a survey, individual dune heights, lengths and migration rates were highly variable, associated with their three‐dimensional geometry and changes in their shape through time. Notwithstanding this variability, there were discernible changes in mean dune height, length and migration rate in response to changing discharge over several days. Changes in mean dune height and length lagged only slightly behind changes in discharge. Therefore, during periods of both steady and unsteady flow, mean dune lengths were quite close to equilibrium values predicted by theoretical models. Mean dune steepnesses were also similar to predicted equilibrium values, except during high, falling flows when the steepness was above that predicted.Variations in mean dune height and length with discharge are similar to those predicted by theory under conditions of low mean dune excursion and discharge variation with a short high water period and long low water period. However, the calculated rates of change of height of individual dunes vary considerably from those measured. Rates of dune creation and destruction were unrelated to discharge variations, contrary to previous results. Instead, creations and destructions were apparently the result of local variations in bed shear stress and sediment transport rate.Observed changes in dune height during unsteady flows agree with theory fairly well at low bed shear stresses, but not at higher bed shear stresses when suspended sediment transport is significant.

Ocean Model Studies of Upper-Ocean Variability at 0°, 160°W during the 1982–1983 ENSO: Local and Remotely Forced Response

Abstract A hindcast of the 1982–1983 ENSO event using a primitive equation ocean circulation model forced by monthly mean wind stresses based on the SADLER pseudostress fields shows very good agreement with observations at 0°, 159°W between June 1982 and March 1983. The hindcast experiment is analyzed to explore the processes that caused the large accelerations, decelerations, and thermal changes observed during this time. Several hindcast experiments incorporating variations of the SADLER wind field and several idealized experiments incorporating a western Pacific westerly wind event are analyzed and compared with the 1982–1983 SADLER hindcast to explore the importance of local and remote forcing, the relative importance of zonal and meridional wind stress changes, and the dynamical signatures of the processes at work. Meridional wind stress changes have little effect on either the zonal velocity or temperature fields. Local zonal wind stress variations can account for the qualitative changes in the uppe...

Interpretation of radar-detected internal layer folding in West Antarctic ice streams

AbstractLow-frequency surface-based radar-profiling experiments on Ice Streams Β and C, West Antarctica, have yielded high-resolution images which depict folding of the internal layers that can aid in the interpretation of ice-stream dynamics. Unlike folding seen in most earlier radar studies of ice sheets, the present structures have no relationship to bedrock topography and show tilting of their axial fold planes in the flow direction. Rather than being standing waves created by topography or local variations in basal shear stress, the data show that these folds originate upstream of the region of streaming flow and are advected into the ice streams. The mechanism for producing folds is hypothesized to be changes in the basal boundary conditions as the ice makes the transition from inland ice to ice-stream flow. Migration of this transition zone headward can then cause folds in the internal layering to be propagated down the ice streams.

Interpretation of radar-detected internal layer folding in West Antarctic ice streams

AbstractLow-frequency surface-based radar-profiling experiments on Ice Streams Β and C, West Antarctica, have yielded high-resolution images which depict folding of the internal layers that can aid in the interpretation of ice-stream dynamics. Unlike folding seen in most earlier radar studies of ice sheets, the present structures have no relationship to bedrock topography and show tilting of their axial fold planes in the flow direction. Rather than being standing waves created by topography or local variations in basal shear stress, the data show that these folds originate upstream of the region of streaming flow and are advected into the ice streams. The mechanism for producing folds is hypothesized to be changes in the basal boundary conditions as the ice makes the transition from inland ice to ice-stream flow. Migration of this transition zone headward can then cause folds in the internal layering to be propagated down the ice streams.

Variation of Local Mechanical Stress During the Different Processing Steps of Ic-Isolation: a Micro-Raman Spectroscopy Study

ABSTRACTLocal mechanical stress introduced in the silicon substrate during the successive steps of poly-buffered local isolation of MOS integrated circuits is studied with micro-Raman spectroscopy. It is shown that the magnitude and the local variation of the stress is highly affected by the different processing steps. After deposition of the nitride mask, the stress can be described as caused by an edge-force. Field oxidation reduces the mask-induced stress but introduces thermal stress from the field oxide. Also the formation of the bird's beak gives rise to additional local tensile stress, especially at the tip of the bird's beak. Removal of the nitride mask results in a partial relaxation: the stress caused by the bird's beak relaxes. In this last stage of the isolation process, the stress image is mostly determined by the field oxide.

Modification of the Shear Lag Analysis for Determination of Elastic Modulus of Short-Fiber (or Whisker) Reinforced Metal Matrix Composites

A major shortcoming of the original shear lag analysis is its inability to provide sufficiently accurate strengthening predictions when the fiber aspect ratio is small. This is due to its neglect of stress transfer across fiber ends and the stress concentrations that exist in the matrix regions near fiber ends. In this paper, a straightforward, yet rigorous, modification of the original shear lag analysis is presented by taking fiber end effects into account and to result in fully closed-form solutions. It is demonstrated that the modification not only results in a correct prediction of the modulus increases in the small aspect ratio regime when compared to finite element results, but is also able to correctly predict the values of interfaciat shear stresses and local stress variations in the matrix and fiber.

Continuation of a deep borehole stress measurement profile near the San Andreas Fault: 2. Hydraulic fracturing stress measurements at Black Butte, Mojave Desert, California

Hydraulic fracturing stress measurements were obtained in the Black Butte drill hole, 18 km northeast of the San Andreas fault in the Mojave Desert, at depths from 251 to 635 m. In all tests the least and greatest horizontal principal stresses (Sh and SH, respectively) exceeded the vertical stress (Sν), indicating a thrust faulting stress regime. A single good‐quality hydraulic fracture impression from 309 m depth indicates an SH direction of N41°E ± 10°. This SH direction should be interpreted with caution because it is based on only one observation. This orientation is fairly compatible with nearby surface stress measurements but is incompatible with most of the hydraulic fracturing stress orientations reported from comparable depths in the Mojave Desert and is not favorable for right‐lateral slip on either the San Andreas fault or NW striking faults present farther to the east. The stress regime measured in the Black Butte hole is comparable to that measured at nearby shallow depths but differs from the strike‐slip or transitional (strike‐slip to thrust faulting) stress regime present at similar depths in two nearby holes: Crystallaire, 4 km northeast of fhe San Andreas fault, and Hi Vista, 32 km northeast of the San Andreas fault. The SH direction measured in these holes is approximately 60° counterclockwise of that observed in the Black Butte hole. The differences in stress magnitudes and orientation among these holes substantiate previous indications of local variations in stress in the upper kilometer of the crust in this area and cast doubt on the validity of linear elastic models in which the effects of the San Andreas fault dominate the stress field in the western Mojave Desert.

Superplastic deformation of sheet test pieces machined from Ti-6Al-4V bar

Sheet tensile test pieces were machined in three orientations from edge textured Ti-6Al-4V bar and tested at temperatures in the range 800 to 975‡ C and at strain rates of 3 × 10−4 and 1.5×10−3 sec−1. Bands of contiguous alpha grains aligned in the rolling direction caused local variations in the flow stress, strain to necking, strain rate sensitivity, plastic strain ratio values and surface roughness. Texture effects were only detected at the lowest test temperature (800‡C) and highest strain rate (1.5×10−3 sec−1).

Deformation mechanism maps and micromechanics of rocks with distributed grain sizes

Conventional deformation mechanism (DM) maps are constructed for single‐valued grain size. When diffusional creep is competitive with power law creep, such maps are a poor guide to rheology and microstructure development in distributed grain size materials because the strain rate dependence on grain size implies wide variations in local stress and/or strain rate. We present DM maps for quartzite with realistic grain size distributions using two bounding models: (1) homogeneous strain rate with local stress varying from grain to grain and (2) homogeneous stress with local strain rate varying. Distributed grain size systems are stronger at low stresses and have larger power law creep fields and larger regions where two or more mechanisms contribute significantly to the total strain rate. Our DM maps do not incorporate grain shape and packing, but we review theoretical work on the effects of these variables and compare rheological predictions with our own for the development of idealized core‐and‐mantle microstructure.

Variational approach to first‐ and second‐order sensitivity analysis of elastic structures

AbstractFor a linear elastic structure, the first variations of arbitrary stress, strain and displacement functionals were explicitly expressed in terms of variations of material stiffness parameters within specified domain, in References 1 and 2, by using the solutions for primary and adjoint systems. In this paper, explicit expressions for second variations are derived for the case when the material stiffness or compliance variations depend on a set of parameters. These expressions arc obtained in terms of variations of stiffness or compliance parameters by using the solutions of two additional sets of adjoint systems. Furthermore, the variation of local stress, strain or displacement is considered. Several illustrative examples are provided for the first‐ and second‐order sensitivity analysis of beams.

Steady state creep of 20% Cr-25% Ni stainless steel with and without a dispersion of tin particles

The steady state creep behaviour of both single phase and TiN dispersion strengthened 20% Cr-25% Ni stainless steel is examined with the object of determining the role of the second phase particles on dislocation network creep. A correlation between the stress/strain rate variation in the two materials can be made by writing. ε ss = A( σ − σ 0) p , where σ is ∼0 and ~80 MPa for single-phase and dispersion hardened steels respectively, and p is ∼5. An expression of this form leads to the prediction of threshold behaviour at σ 0, but the creep rate data indicate that steady state creep also occurs below this stress. Microstructural observations are described which suggest that σ 0 in the TiN bearing alloy can be identified with σ p , the Orowan stress. The Orowan mechanism cannot operate below σ p , but an alternative mode of dislocation bypass around particles is available, which leads to a mechanistic transition at a stress σ gt where the rates of the two processes are the same. The stress/dislocation density relationship is investigated, and it is found that the density p in the dispersion hardened alloy becomes constant below the Orowan stress at a density ( p 0) such that the average network link length is equal to the interparticle spacing. Further, the strain rate/dislocation density variation in single phase material at high stress appears to be such that ε α σ − σ s pα p p 2 while at low stresses there is an excess of dislocations. It is argued that writing ε α ρ − ρ 0 p 2 with ρp 0 the annealed-in density, allows the strain rate to be self-consistent function of the active dislocation content over the entire stress range. Moreover, treating the data from the two-phase steel in the same manner reduces the ε/( ρ − ρ 0) points from both alloys to a single curve. The density ρ 0 is suggested to arise as a result of stress relaxation where dislocations are held up at hard parts of the microstrucure. The stress relaxation produces an increase in the total dislocation line length, but a reduction in the stored energy, so that the driving force for recovery is reduced at a given total density. The relaxation structures themselves must recover, and this is likely to happen over the microstructural wavelength of the plastic inhomogeneity which is not only responsible for the presence of the geometrically necessary dislocations, but which also determines the content of annealed material. The spatial inhomogeneity of the dislocation density can be described in terms of a steady-state internal stress distribution which acts so as to compensate for variations in local flow stress. The threshold behaviour, however, is suggested to arise because the TiN particles are undeformable. The Orowan stress always therefore has to be exceeded before the network model of dislocation creep can be at all appropriate. However, the measured variations in dislocation density with stress imply that the creep rate can be correlated with the dislocation density, as in the network model, if the effects of plastic relaxation are taken into account.