Mechanical Modeling of Thin Films and Cover Plates Bonded to Graded Substrates

In this study, the contact problems of thin films and cover plates are considered. In these problems, the loading consists of any one or combination of stresses caused by uniform temperature changes and temperature excursions, far field mechanical loading, and residual stresses resulting from film processing or welding. The primary interest in this study is in examining stress concentrations or singularities near the film ends for the purpose of addressing the question of crack initiation and propagation in the substrate or along the interface. The underlying contact mechanics problem is formulated by assuming that the film is a “membrane” and the substrate a graded elastic continuum, and is solved analytically by reducing it to an integral equation. The calculated results are the interfacial shear stress between the film and the graded substrate, the Mode II stress intensity factor at the end of the film, and the axial normal stress in the film. The results indicate that grading the material properties of the substrate helps to decrease the film stresses and the stress intensity factors at the free edges and to lower the axial normal stresses at the midsection where the film is most likely to crack.

PREDICTION OF THE FATIGUE STRENGTH OF NODULAR CAST IRONS UNDER COMBINED LOADING

A criterion was proposed for the prediction of the multiaxial fatigue strength of specimens containing small holes. The criterion was applied to nodular cast irons containing graphite nodules and small casting defects such as microshrinkage cavities. Combined axial and torsional fatigue tests were carried out to examine the influences of torsional shear stress amplitude, axial normal stress amplitude, the ratio of these stress amplitudes, phase difference, and mean stress. The materials investigated were nodular cast irons with a ferrite matrix, JIS FCD400, and a pearlite matrix, JIS FCD700. A method for the prediction of the lower bound of fatigue strength was presented. Reasonable agreement between predictions and experimental results was obtained.

Variable Conductance Two-Phase Closed Flat Plate Thermosyphon With Binary Mixture

In this paper the variable conductance heat transfer in a flat plate thermosyphon has been considered. For this purpose the governing equations including mass and momentum conservation laws are solved numerically. It should be noted that liquid-film momentum advection, axial normal stress and interfacial shear stress were typically included and shown to be important to the thermosyphon performance. It is found that total system pressure and mean vapor temperature at different concentrations of mixture are nearly constant for a special range of absorbed power in evaporator. The obtained numerical results are in good agreement with available experimental data.

3D Measurements of Deterministic Stresses Within a Rotor-Stator Gap at Mid-Span and Tip Regions

Stereoscopic Particle Image Velocimetry is used for measuring the distributions of the deterministic stresses, in the tip and mid-span regions, within the second stage rotor-stator gap of a two-stage axial turbomachine. This effort extends our previous two-dimensional measurements to study the dynamics of deterministic stresses in a multistage turbomachine using experimental data. All three components of the velocity vector, and all six components of both the turbulent and deterministic stress tensors are obtained at a Reynolds number of 370,000 based on the tip speed and the rotor blade chord, and in an optically unobstructed facility that uses blades and fluid with matched optical indices of refraction. Results at 50% show that although the radial velocity levels are about an order of magnitude smaller than the axial and lateral velocity levels, the flow is not exactly two-dimensional. The wake kinking phenomenon and the presence of chopped-off stator wake segments introduce three-dimensionality to the flow. The radial velocity fluctuations are high around the kink region, and get even higher when the potential field of the stator blade starts to interact with the kink zone. In general, the turbulent normal stresses are higher than the deterministic normal stresses while the turbulent and deterministic shear stress levels are in the same order of magnitude. The flow at 90% span is dominated by the tip vortices, which create high levels of non-uniformities in the distributions of all three velocity components. The tip vortex loses its structure when it gets close to the pressure side of the following rotor blade and undergoes a possible spiral-type vortex breakdown. The meandering and convection of the tip vortices contribute to the elevated levels of average-passage turbulence and deterministic stresses along the tip vortex transport direction. The deterministic axial normal stress is higher than the turbulent axial normal stress; the deterministic lateral normal stress is initially higher, but it quickly drops down to turbulent lateral normal stress levels; and the deterministic radial normal stress is initially close to turbulent radial normal stress levels, but it decays relatively quickly and becomes less than the turbulent radial normal stress levels further downstream. The deterministic shear stress components are 5 to 10 times higher than the turbulent shear stress components.

Fully developed viscous and viscoelastic flows in curved pipes

Some h-p finite element computations have been carried out to obtain solutions for fully developed laminar flows in curved pipes with curvature ratios from 0.001 to 0.5. An Oldroyd-3-constant model is used to represent the viscoelastic fluid, which includes the upper-convected Maxwell (UCM) model and the Oldroyd-B model as special cases. With this model we can examine separately the effects of the fluid inertia, and the first and second normal-stress differences. From analysis of the global torque and force balances, three criteria are proposed for this problem to estimate the errors in the computations. Moreover, the finite element solutions are accurately confirmed by the perturbation solutions of Robertson & Muller (1996) in the cases of small Reynolds/Deborah numbers.Our numerical solutions and an order-of-magnitude analysis of the governing equations elucidate the mechanism of the secondary flow in the absence of second normal-stress difference. For Newtonian flow, the pressure gradient near the wall region is the driving force for the secondary flow; for creeping viscoelastic flow, the combination of large axial normal stress with streamline curvature, the so-called hoop stress near the wall, promotes a secondary flow in the same direction as the inertial secondary flow, despite the adverse pressure gradient there; in the case of inertial viscoelastic flow, both the larger axial normal stress and the smaller inertia near the wall promote the secondary flow.For both Newtonian and viscoelastic fluids the secondary volumetric fluxes per unit of work consumption and per unit of axial volumetric flux first increase then decrease as the Reynolds/Deborah number increases; this behaviour should be of interest in engineering applications.Typical negative values of second normal-stress difference can drastically suppress the secondary flow and in the case of small curvature ratios, make the flow approximate the corresponding Poiseuille flow in a straight pipe. The viscoelasticity of Oldroyd-B fluid causes drag enhancement compared to Newtonian flow. Adding a typical negative second normal-stress difference produces large drag reductions for a small curvature ratio δ = 0.01; however, for a large curvature ratio δ = 0.2, although the secondary flows are also drastically attenuated by the second normal-stress difference, the flow resistance remains considerably higher than in Newtonian flow.It was observed that for the UCM and Oldroyd-B models, the limiting Deborah numbers met in our steady solution calculations obey the same scaling criterion as proposed by McKinley et al. (1996) for elastic instabilities; we present an intriguing problem on the relation between the Newton iteration for steady solutions and the linear stability analyses.

End Effects in Twisted Cord-Rubber Composites

This paper investigates the cord-matrix load transfer problem in twisted cord-rubber composites. The central feature of the study is to ascertain the polarizing effects of twist-induced coupling of the axial loads and torque. Particular emphasis is given to the end problem, namely the transition between the axial-circumferential shear stress-dominated end region and the axial normal stress and torque-controlled far-from-end zone. This is achieved through the development of both a closed form analytic formulation and its corroboration by a detailed finite element simulation.

An Analysis of the Thin-Walled Torsion Specimen

A detailed finite element analysis has been conducted of the thin-walled torsion specimen. This specimen, when properly gripped, provides an approximation to the simple shear deformation field. Variations through the thickness of the specimen are small for the shear stress but can be large for the axial normal stress. Plastic deformation extends into the shoulder region requiring a correction factor to be used when converting the applied twist at the grips to average shear strain across the gauge section. This correction factor can be numerically quantified and used in data reduction.

Low Buckling Stresses of Axially Compressed Circular Cylindrical Shells of Finite Length

Exact solutions are derived of the classical differential equations defining the deformations of axially compressed thin-walled circular cylindrical shells. The end conditions along the circular edges are assumed as the vanishing (a) of the radial displacement; (b) of the longitudinal bending moment; (c) of the variation in the axial normal stress resultant; and (d) of the circumferential membrane shear stress resultant. Under these conditions of simple support the critical value of the uniformly distributed axial normal stress is one half the classical critical value.