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Analysis of shear and normal strain effects on weak turbulence and turbulent heat transfer using two point correlation equations obtained from Navier-Stokes and energy equations
The method of strain range partitioning was applied to a series of torsional fatigue tests conducted on tubular 304 stainless steel specimens at 1200 F (649 C). Creep strain was superimposed on cycling strain, and the resulting strain range was partitioned into four components; completely reversed plastic shear strain followed by creep strain, creep strain followed by plastic strain and completely reversed creep strain. Each strain component was related to the cyclic life of the material. The paper describes the experimental procedure used to achieve strain partitioning and the torsional test results are compared to those obtained from axial tests. The damaging effects of the individual strain components were expressed by a linear life fraction rule. The shear strain plastic component showed the least detrimental factor when compared to creep strain reversal by plastic strain. In the latter case, a reduction of torsional fatigue life in the order of magnitude of 1.5 was observed.
The questions of relative motions of large segments of Ganymede's lithosphere and of the effect of any motions on grooved terrain formation are reexamined. Resolvable furrows in both hemispheres were mapped in great detail using Voyager 1 and 2 images and U.S. Geological Survey controlled shaded-relief quadrangle maps. Estimates of the Galileo Regio and Marius Regio poles of furrow concentricity indicate a considerable westward offset of the Galileo Regio pole, suggesting the possibility of about 500-km of left-lateral offset of the two areas. There is evidence that shear deformation was concentrated along a major structural lineament which follows a small circle and encloses Galileo Regio, and that a smaller amount of distributed shear occurred across an adjacent 500- to 1500-km-wide band. The results indicate that either widespread shear strain or the shear's driving mechanism may have had a long-term effect on patterns of deformation of Ganymede's lithosphere.
The Foam Optics and Mechanics (FOAM) project will exploit the microgravity environment to more accurately measure the rheological and optical characteristics of wet aqueous foams. Using both rheology and laser light scattering diagnostics, the goal is to quantify the unusual elastic character of foams in terms of their underlying microscopic structure and dynamics. Of particular interest is determining how the elastic character vanishes, i.e., how the foam 'melts' into a simple viscous liquid, as a function of both increasing liquid content and increasing shear strain rate. The unusual elastic character of foams will be quantified macroscopically by measurement of the shear stress as a function of shear strain rate and of time following a step strain. Such data will be analyzed in terms of a yield stress, shear moduli, and dynamical time scales. Microscopic information about bubble packing and rearrangement dynamics, from which the macroscopic non-Newtonian properties ultimately arise, will be obtained non-invasively by multiple-light scattering: diffuse transmission spectroscopy (DTS) and diffusing wave spectroscopy (DWS). Quantitative trends with materials parameters, most importantly average bubble size and liquid content, will be sought in order to elucidate the fundamental connection between the microscopic structure and dynamics and the macroscopic rheology.
Two hybrid methods of deformation analysis combining moire interferometry and finite element techniques are introduced. The hybrid methods are applied to determine the strain fields in the test section of a composite cruciform specimen in order to evaluate the uniformity of the shear strain field. Both methods show that there are significant shear strain gradients in the specimen test section. One of the hybrid methods - the full-field analysis using the random-node mesh generator - detects the presence of material property nonuniformity which is assumed uniform in the boundary-node method.
A convolutional neural network was used to enhance the localization of strain and stress for a generalized method of cells model of a metallic microstructure. Enhanced shear strains, measured in terms of the linear regression coefficients as a function of ground truth strains, were improved from inaccurate and uncorrelated (slope=0.003, Rsq=0.000) to accurate and well correlated (slope=0.890, Rsq=0.882) relative to ground truth (slope=1.0, Rsq=1.0). In applying the convolutional neural network, a convolutional stride of 1.0 (padding=’same’) was only modestly effective while strides of 2 or 3 were more effective yet at higher cost. Additional convolutional layers were generally more expensive than additional dense layers, often with limited benefit. The accuracy of enhanced localized shear strains and stress is expected to yield benefits for damage progression models, especially in the context of hierarchical multi-scale methods where the generalized method of cells is applied at the intermediate scale.
A {1,2}-order theory for laminated composite and sandwich plates is extended to include thermoelastic effects. The theory incorporates all three-dimensional strains and stresses. Mixed-field assumptions are introduced which include linear in-plane displacements, parabolic transverse displacement and shear strains, and a cubic distribution of the transverse normal stress. Least squares strain compatibility conditions and exact traction boundary conditions are enforced to yield higher polynomial degree distributions for the transverse shear strains and transverse normal stress through the plate thickness. The principle of virtual work is used to derive a 10th-order system of equilibrium equations and associated Poisson boundary conditions. The predictive capability of the theory is demonstrated using a closed-form analytic solution for a simply-supported rectangular plate subjected to a linearly varying temperature field across the thickness. Several thin and moderately thick laminated composite and sandwich plates are analyzed. Numerical comparisons are made with corresponding solutions of the first-order shear deformation theory and three-dimensional elasticity theory. These results, which closely approximate the three-dimensional elasticity solutions, demonstrate that through - the - thickness deformations even in relatively thin and, especially in thick. composite and sandwich laminates can be significant under severe thermal gradients. The {1,2}-order kinematic assumptions insure an overall accurate theory that is in general superior and, in some cases, equivalent to the first-order theory.
Global plate models predict about 56 mm/yr of motion between the North American and Pacific plates along the plate boundary in southern California, while geodetic and Holocene geological data suggest only 34 mm/yr on the San Andreas fault. Deformation in the Great Basin does not explain this discrepancy, and it has been suggested that faulting in the offshore of southern California could account for some of the discrepancy. Evidence of deformation in the offshore region of southern California is most abundant in the Santa Barbara Channel. Geological investigations of folding and faulting in this region, as well as earthquake investigations, indicate north-south shortening across the channel on the order of 10 to 20 mm/yr. The most rapid rates occur to the east of the channel in the Ventura Basin. South of the Santa Barbara Channel, though, evidence for deformation is limited to seismicity studies which are sparse. Seismic events are abundant in this area, but their implication for the amount of deformation in the offshore is unclear. GPS measurements made between June 1986 and May 1988 have been used to obtain vector positions for several stations at which historical first order triangulation observations were performed between the late 1800's and the mid 1900's between the coast of southern California and the nearby offshore islands. By comparing the spheroidal angles obtained from the GPS positions with the the previously observed triangulation data, shear strain rates can be calculated for the region using Frank's method. These results seem to suggest that shear strain deformation occurs in the offshore of southern California as a result of north to north-west shortening. That deformation is most active in the Santa Barbara Channel region and least active between Catalina and San Nicholas islands. Just how much of the missing plate motion can be accounted for by this deformation is not known at this time and will have to await further analysis.
A simple two node, linear, finite strip plate bending element based on Mindlin-Reissner plate theory for the analysis of very thin to thick bridges, plates, and axisymmetric shells is presented. The new transverse shear strains are assumed for constant distribution in the two node linear strip. The important aspect is the choice of the points that relate the nodal displacements and rotations through the locking transverse shear strains. The element stiffness matrix is explicitly formulated for efficient computation and ease in computer implementation. Numerical results showing the efficiency and predictive capability of the element for analyzing plates with different supports, loading conditions, and a wide range of thicknesses are given. The results show no sign of the shear locking phenomenon.
The shear strain rates in the Diablo Range of California have been calculated, and the slip rate along the Calaveras and Paicines faults in Central California have been estimated, on the basis of triangulation and trilateration data from two geodetic networks located between the western edge of the Great Valley and the San Andreas Fault. The orientation of the principal compressive strain predicted from the azimuth of the major structures in the region is N 25 deg E, leading to an average shear strain value that corresponds to a relative shortening rate of 4.5 + or - 2.4 mm/yr. It is inferred that the measured strain is due to compression across the fold of this area. The hypothesized uniform, fault-normal compression within the Coast Ranges is not supported by these results.
We have measured the deformation in the Ventura basin region, southern California, with Global Positioning System (GPS) measurements carried out over 4.6 years between 1987 and 1992. The deformation within our network is spatically variable on scales of tens of kilometers, with strain rates reaching 0.6 +/- 1 micro-rad/yr in the east-central basin. Blocklike rotations are observed south and northwest of the basin where the maximum shear strain rates are an order of magnitude lower (0.06 +/- 1 micro-rad/yr to the south). We also observed clockwise rotations of 1 deg - 7 deg/m.y. Shear strain rates determined by comparing angle changes from historical triangulation spanning several decades and GPS measurements give consistent, though less precise, results. The geodetic rates of shortening across the basin and Western Transverse Ranges are lower than those estimated from geological observations, but the patterns of deformation from the two methods agree qualitatively.
A unidirectional graphite epoxy material (AS4/3501-6) was characterized at strain rates ranging from 5 x 10(exp 6) s(exp -1) to 5(exp -1), at room temperature and at 128 C. Results are presented in the form of stress-strain curves to failure. The longitudinal properties remain nearly unchanged with strain rate and temperature. The transverse modulus increases with strain rate but decreases with temperature. The transverse strength and transverse ultimate tensile strain have a positive rate sensitivity at low rates, which changes to negative at intermediate rates and returns to positive rate sensitivity at the highest rates tested. A temperature-time equivalence principle was applied and master curves were obtained for the transverse mechanical properties. The in-plane shear modulus and in-plane shear strength have a positive rate sensitivity. The ultimate intralaminar shear strain has a positive rate sensitivity at low rates, which changes to negative at high rates. At the elevated temperature of 128 C, the ultimate shear strain is 25 to 30 percent higher than the room temperature value, but its strain rate dependence is moderate.
A new (1,2)-order theory is proposed for the linear elasto-static analysis of laminated composite plates. The basic assumptions are those concerning the distribution through the laminate thickness of the displacements, transverse shear strains and the transverse normal stress, with these quantities regarded as some weighted averages of their exact elasticity theory representations. The displacement expansions are linear for the inplane components and quadratic for the transverse component, whereas the transverse shear strains and transverse normal stress are respectively quadratic and cubic through the thickness. The main distinguishing feature of the theory is that all strain and stress components are expressed in terms of the assumed displacements prior to the application of a variational principle. This is accomplished by an a priori least-square compatibility requirement for the transverse strains and by requiring exact stress boundary conditions at the top and bottom plate surfaces. Equations of equilibrium and associated Poisson boundary conditions are derived from the virtual work principle. It is shown that the theory is particularly suited for finite element discretization as it requires simple C(sup 0)- and C(sup -1)-continuous displacement interpolation fields. Analytic solutions for the problem of cylindrical bending are derived and compared with the exact elasticity solutions and those of our earlier (1,2)-order theory based on the assumed displacements and transverse strains.
The potential of the transportable laser ranging system for monitoring the ground deformation around satellite ranging stations and other geodetic control points was examined with emphasis on testing the usefulness of the relative alteration technique. The temporal variation of the ratio of the length of each survey line to the mean length of all survey lines in a given area is directly related to the mean shear strain rate for the area. The data from a series of experimental measurements taken over the Los Angeles basin from a TLRS station at Mt. Wilson show that such ratios can be determined to an accuracy of one part in 10 million with a measurement program lasting for three days and without using any corrections for variations in atmospheric conditions. A numerical experiment using a set of hypothetical data indicates that reasonable estimates of the present shear strain rate and the direction of the principal axes in southern California can be deduced from such measurements over an interval of one to two years.
Results are given of an analysis of wing and horizontal-tail spar strains measured on a twin-engine light transport airplane which was modified for the installation of a control system to alleviate airplane motions in turbulent air and thus improve passenger comfort. From a sample of the measurements obtained in flight through clear-air turbulence, normal acceleration at the airplane center of gravity was reduced 43 percent, wing main-spar bending strains were reduced, and wing-spar shear strains were increased. Horizontal-tail shear and bending strains were increased. Measurements of aerodynamic loads obtained in a pull-up with the gust-alleviation system in operation are also presented.
A technique for conducting strain-controlled, thermomechanical, axial-torsional fatigue tests on thin-walled tubular specimens was developed. Three waveforms of loading, namely, the axial strain waveform, the engineering shear strain waveform, and the temperature waveform were required in these tests. The phasing relationships between the mechanical strain waveforms and the temperature and axial strain waveforms were used to define a set of four axial-torsional, thermomechanical fatigue (AT-TMF) tests. Real-time test control (3 channels) and data acquisition (a minimum of 7 channels) were performed with a software program written in C language and executed on a personal computer. The AT-TMF testing technique was used to investigate the axial-torsional thermomechanical fatigue behavior of a cobalt-base superalloy, Haynes 188. The maximum and minimum temperatures selected for the AT-TMF tests were 760 and 316 C, respectively. Details of the testing system, calibration of the dynamic temperature profile of the thin-walled tubular specimen, thermal strain compensation technique, and test control and data acquisition schemes, are reported. The isothermal, axial, torsional, and in- and out-of-phase axial-torsional fatigue behaviors of Haynes 188 at 316 and 760 C were characterized in previous investigations. The cyclic deformation and fatigue behaviors of Haynes 188 in AT-TMF tests are compared to the previously reported isothermal axial-torsional behavior of this superalloy at the maximum and minimum temperatures.
A simple method is developed for solving plane-plastic-stress problems with axial symmetry in the strain-hardening range which is based on the deformation theory of plasticity employing the finite-strain concept. The equations defining the problems are first reduced to two simultaneous nonlinear differential equations involving two dependent variables: (a) the octahedral shear strain, and (b) a parameter indicating the ratio of principal stresses. By multiplying the load and dividing the radius by an arbitrary constant, it is possible to solve these problems without iteration for any value of the modified load. The constant is determined by the boundary condition. This method is applied to a circular membrane under pressure, a rotating disk without and with a central hole, and an infinite plate with a circular hole. Two materials, inconel x and 16-25-6, the octahedral shear stress-strain relations of which do not follow the power law, are used. Distributions of octahedral shear strain, as well as of principal stresses and strains, are obtained. These results are compared with the results of the same problems in the elastic range.
Displacement fields in a thick adherend lap joint were measured by high-sensitivity moire interferometry. Contour maps of in-plane U and V displacements were obtained across adhesive and adherend surfaces. Loads ranged from a modest load to a near-failure load. Quantitative results are given for displacements and strains in the adhesive and along the adhesive/adherend boundary lines. The results show nearly constant shear strain in the adhesive, nonlinear strains as a function of load or average shear stress, and viscoelastic or time-dependent response. Longitudinal normal strains in the adhesive are nearly two orders of magnitude less than the shear strains. With its subwavelength displacement resolution and high spatial resolution, moire interferometry is especially well suited for deformation studies of adhesive joints.