Solution of problems involving the stress state of composite materials with curved layers in the geometrically nonlinear statement

Mechanics Institute, Academy of Sciences of the Ukraine, Kiev. Institute of Mathematics and Mechanics, Academy of Sciences of the Azerbaijan Republic, Baku. Translated from Prikladnaya Mekhanika, Vol. 28, No. 6, pp. 3–8, June, 1992.     

A simple slurry consolidometer designed for the estimation of the consistency limits of soils

An inexpensive slurry consolidometer design is described that uses porous polyethylene as the permeable barrier for sample dewatering (maximum effective stress of 200 kPa) and permits monitoring of sample pore-water pressures less than 100 kPa with a portable pressure transducer. The instrument is applied in this study to the consolidation-based estimation of the Atterberg soil consistency limits of both agricultural soils and till and glaciolacustrine materials (clay fraction predominantly Ca-saturated illites) sampled from sonic boreholes. All soils originated from southwestern Ontario, Canada. With the normally consolidated (virgin) compression line expressed as a w(logσ') function, the A.S.T.M. liquid and plastic limits of the borehole soils were found to occupy relatively fixed positions on the VCL at mean effective stresses of about 61 kPa and 0.42 MPa, respectively. Marginally plastic and non-plastic soils could be distinguished as having compression line slopes approaching zero. The effective stress at the liquid limit decreased logarithmically from 61 kPa with increasing organic carbon content in the agricultural soils. Consolidated slurries of all soils investigated that were clearly plastic exhibited a mean drop-cone penetration depth of approximately 13 mm at the A.S.T.M. liquid limit, a significant departure from the British Standard of 20 mm. Slurry consolidation can be used as a sample preparation method for measurement of the liquid limit by the drop-cone or one-point A.S.T.M. procedures. It has also shown potential as a procedural alternative for the estimation of both test indices, mostly for geotechnical applications. It is probable that this unified test protocol must be recalibrated for soils where the dominant clay minerals and saturating bases are different from those in this study.     

Interaction between the effects of local and overall imperfections on the buckling of elastic columns

A. van derNeut has studied the buckling of elastic columns made from thin-walled members, with particular reference to the effects of imperfections. In this paper, a graphical method is used to extend his work and to make an exhaustive study of the combined effects of both ‘local’ and ‘overall’ imperfections. The resulting picture is remarkably simple, and the effects of imperfections are well described by the celebrated Perry formula in conjunction with a single imperfection parameter compounding simply the local and overall imperfections. Experiments on small-scale rubber model columns substantiate the main results of the theoretical analysis.     

The experimental determination of velocity distribution in annular flow

In the study of the flow of a fluid through an annular gap, the outer surface of which is stationary while the inner surface may be rotated, it is necessary to be able to accurately determine the velocity profiles obtaining in the axial, tangential, and radial directions of flow.

A method is described for this purpose employing hot-wire anemometry techniques and typical profiles are presented for each of the above flow directions. In the case of pure axial flow, a comparison is made between experimental and theoretical results, showing a close correspondence.     

Recoil in macromolecular solutions according to rigid dumbbell kinetic theory

A macromolecular solution is represented by the simple model of rigid dumbbells suspended in a Newtonian fluid with Brownian motion included. Hydrodynamic interaction is not taken into account. It is found that for this model there will be recoil after the cessation of steady shearing flow. The ultimate shear recovery S _∞ is developed as a power series in κ^?, the shear rate prior to the cessation of the steady shear flow: $$S_\infty = (\theta _0 /2\eta _0 ) \kappa ^\user1{ - } + O(\kappa ^\user1{ - } )^3$$ where η₀ and θ₀ values of the viscosity and primary normal stress functions respectively at zero-shear rate. The coefficient of the term in (κ^?)³ is calculated. In addition, the behavior of the normal stresses during the recoil process is found; during recoil τ₂₂?τ₃₃ has the opposite sign from τ₁₁?τ₂₂.     

Evaluation of three-dimensional stresses in shrink-fit problems by scattered-light photoelasticity

Stresses caused by shrink fits are commonly evaluated by using Lame's solution or by other analytical methods in which it is assumed that the radial stresses on the surface of contact are distributed uniformly, or in some stepwise manner, and that friction forces between the bodies are zero. These assumptions were not necessary in the experimental problem solved. Heretofore, no experimental techniques have been available to check the existing theories on a three-dimensional basis. The stresses which result when a short, hollow, thick-walled cylinder is shrunk over a shaft which is a solid shaft or a thick-walled, hollow shaft were determined. Equipment and techniques using scattered-light three-dimensional photoelasticity with a laser light source were developed and applied.     

A torsional creep apparatus

Summary This paper describes a torsional creep apparatus for the determination of the creep compliance in shear as a function of time. The instrument is suitable for the measurement of compliances below 5·10^–8 m²/N, in the time range between 1 and 10⁵ seconds. Within five minutes and with an accuracy of 1 C, the temperature of the specimen can be adjusted to any value between –175 and –200 C. From the torsional creep measurements can be calculated the dynamic shear modulus and the corresponding damping. The lowest damping, determined in this way, is several times 10^–3.

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Zusammenfassung Ein Apparat zur Messung des Torsions-Kriechverhaltens wird beschrieben. Das Instrument ist zur Bestimmung von Nachgiebigkeiten kleiner als 5·10^–5 m²/N im Zeitbereich zwischen 1 und 10⁵ Sekunden geeignet. Die Temperatur der Probe läßt sich innerhalb 5 Minuten und mit einer Genauigkeit von 1 C auf jeden Wert zwischen –175 und –200 C einstellen. Aus der gemessenen Kriechfunktion können der dynamische Schubmodul und die dynamische Dämpfung berechnet werden. Eine untere Grenze für die Dämpfung, die man auf diese Weise noch bestimmen kann, ist einige Male 10^–3.

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The work was partly sponsored by the Office of Naval Research, Washington, D. C., under contract number N 62558-3884.     

Influence of the hall effect on development of rotational MHD flow in a flat channel

In an experimental study of the heat transfer from a partially ionized gas it was found that the heat flux to the wall for flow of an electrically conducting gas in a circular tube located in a magnetic field of a solenoid depends not only on the magnitude of the magnetic field but also on the field orientation [1]; with the magnetic field parallel to the velocity the heat transfer is reduced by 15%, with antiparallel orientation it is reduced by only 1% in comparison with the heat transfer without the magnetic field. No explanation for this was given either in [1] or in the subsequent discussion [2]; moreover, on the basis of the constructed equations [1] this effect cannot be obtained at all, since the solution of the equations clearly is not changed by a change of the field sign. In the following we attempt to explain this effect by the processes which take place during the development of rotational flow of an anisotropically conducting medium. The idea of the possibility of such an explanation for this effect was proposed in general form in the survey paper [3].The detailed calculation of the development of MHD flows has been made previously only for the case of a transverse magnetic field and very simple channel geometry (see, for example, the survey [3]).In all the considered problems the components of the electrical field which appeared in the motion equations were known with an accuracy to constants from symmetry considerations. Therefore, under the assumption of smallness of the induced magnetic field these problems reduced simply to the solution of the equation of motion with additional terms which are linear in the velocity. In the present paper we construct an approximate simultaneous solution of a system consisting of the motion equations and the equation for the electrical potential.     

A Binary Model of textile composites: III high failure strain and work of fracture in 3D weaves

Prior experiments have revealed exceptionally high values of the work of fracture (0.4-) in carbon/epoxy 3D interlock woven composites. Detailed destructive examination of specimens suggested that much of the work of fracture arose when the specimens were strained well beyond the failure of individual tows yet still carried loads . A mechanism of lockup amongst broken tows sliding across the final tensile fracture surface was suggested as the means by which high loads could still be transferred after tow failure. In this paper, the roles of weave architecture and the distribution of flaws in the mechanics of tow lockup are investigated by Monte Carlo simulations using the so-called Binary Model. The Binary Model was introduced previously as a finite element formulation specialised to the problem of simulating relatively large, three-dimensional segments of textile composites, without any assumption of periodicity or other symmetry, while preserving the architecture and topology of the tow arrangement. The simulations succeed in reproducing all qualitative aspects of measured stress-strain curves. They reveal that lockup can indeed account for high loads being sustained beyond tow failure, provided flaws in tows have certain spatial distributions. The importance of the interlock architecture in enhancing friction by holding asperities on sliding fibre tows into firm contact is highlighted.     

Use of caged fluorescent dyes for the study of turbulent passive scalar mixing

The non-intrusive initialization of a flow field with distinct and spatially segregated scalar components represents a significant experimental difficulty. Here a new technique is described which makes possible the non-intrusive initialization of a spatially binary passive scalar field in a laminar or turbulent flow field. This technique uses photoactivatable (caged) fluorescent dyes dissolved in the flow medium. The scalar field within the flow field is tagged or initialized by uncaging the appropriate regions with an ultraviolet excimer laser. Mixing between the tagged and untagged regions is quantified using standard laser induced fluorescence techniques. The method is currently being used to study mixing in a turbulent pipe flow.