Thinning and thickening effects induced by shearing in lecithin solutions of polymer-like micelles

 The effects of shear flow on the lecithin organogels consisting of reverse polymer-like micelles have been investigated by dynamic rheology. It was established that the shear effects depended on the molar ratio of water to lecithin that determined the micellar type in the system. For an organogel with linear flexible polymer-like micelles, thinning was observed. The main features of the rheological behavior bore a resemblance to previously investigated aqueous systems made up of similar but direct polymer-like surfactant micelles. The thinning effects are explicable on the basis of alignment of micellar aggregates along the flow direction and their disentanglement. An organogel with branched micelles did not demonstrate any notable response to the shearing. Unusual behavior was noticed in the case of a jelly-like phase that included the highest amounts of water. The applied steady shear flow induced a thickening effect. This was followed by restructuring of the micellar system at the level of polymer-like micelles and their network. The shearing effects were characterized by slow kinetics. In addition, the system did not revert to the original state after the cessation of steady shear flow even within 8 h. Measurements performed in an oscillation regime on this system showed that shearing should promote a substantial growth of the polymer-like micelles and affect their alignment. Received: 18 May 1999 Accepted: 27 March 2000     

Sliding friction in the presence of ultrasonic oscillations: superposition of longitudinal oscillations

Summary  It was often observed that friction forces can be reduced significantly if ultrasonic oscillations are superposed to the macroscopic sliding velocity. This phenomenon can be used to improve machining processes by addition of ultrasonic vibration to tools or workpieces, and forms the basis for many processes of ultrasonic machining. On the other hand, ultrasonic vibrations can be used to generate motion. The thrusting force of ultrasonic motors is provided to the rotor through friction. In the present paper, a simple theoretical model for friction in the presence of ultrasonic oscillations is derived theoretically and validated experimentally. The model is capable of predicting the reduction of the macroscopic friction force as a function of the ultrasonic vibration frequency and amplitude and the macroscopic sliding velocity. Received 22 November 2000; accepted for publication 6 February 2001     

Stability of equilibrium states in a simple system with unilateral contact and Coulomb friction

The aim of this paper is to study the stability of equilibrium states in a mechanical system involving unilateral contact with Coulomb friction. Since the assumptions made in classical stability theorems are not satisfied with this class of systems, we return to the basic definitions of stability by studying the time evolution of the distance between a given equilibrium and the solution of a Cauchy problem where the initial conditions are in a neighborhood of the equilibrium. It was recently established that the dynamics is well posed in the case of analytical data. In the present study, we focus in particular on the stability of the equilibrium states under a constant force and deal only with a simple mass-spring system in .     

Thermal instability of a porous medium with relaxation and inertia in the presence of Hall effects

Summary  The thermal instability of a Rivlin–Ericksen fluid in a porous medium is considered in the presence of a uniform vertical magnetic field to include the effect of Hall currents. For the case of stationary convection, the magnetic field has a stabilizing effect on the system, whereas the Hall current has a destabilizing effect on the system. The medium permeability has both stabilizing and destabilizing effects, depending on the Hall parameter M. The kinematic viscoelasticity has no effect on stationary convection. Graphs have been plotted by giving numerical values to the parameters, to depict the stability characteristics. The magnetic field (and corresponding Hall currents) introduces oscillatory modes in the system, which would be nonexistent in their absence. The sufficient conditions for the nonexistence of overstability are also obtained. Received 20 May 1999; accepted for publication 8 March 2000     

Influence of spring dynamics and friction on a spring-actuated cam system

Summary  The paper investigates two important aspects, friction and spring motion, of the dynamics of a spring-actuated cam system. The characteristics of the friction on the camshaft are analyzed using the nonlinear pendulum experiment, while the parameters of the friction model are estimated using the optimization technique. The analysis reveals that the friction of the camshaft depends on stick–slip, Stribeck effect and viscous damping. Spring elements are found to have much influence on the dynamic characteristics. Hence, they are modeled as four-degrees-of-freedom lumped masses with equivalent springs. The lumped masses and equivalent springs are obtained to match the static stiffness and natural frequency of the actual spring. The appropriateness of the derived friction and spring model are verified by its application to a vacuum circuit-breaker mechanism of the cam-follower type. Received 23 March 2000; accepted for publication 21 November 2000     

Driving forces and kinking of an oblique crack in bonded nonhomogeneous materials

Summary  Plane elasticity solutions are presented for the problem of an oblique crack in two bonded media. The material model under consideration consists of a homogeneous half-plane with an arbitrarily oriented crack and a nonhomogeneous half-plane. The Fourier integral transform method is employed in conjunction with the coordinate transformations of field variables in the basic elasticity equations. Formulation of the crack problem results in having to solve a system of singular integral equations for arbitrary crack surface tractions. A crack perpendicular to or along the bonded interface between the homogeneous and nonhomogeneous constituents arises as a limiting case. In the numerical results, the values of mixed-mode stress intensity factors are provided for various combinations of relevant geometric and material parameters of the bonded media. Subsequently, the infinitesimal kinks from the tips of a main crack are presumed, with the corresponding local driving forces being evaluated in terms of the stress intensities of the main crack. The criterion of maximum energy release rate is applied with the aim of making some conjectures concerning the likelihood of kinking and the probable kink direction based on the approximation of local homogeneity and brittleness of the crack-tip behavior. Received 25 September 2001; accepted for publication 13 February 2002     

Generalized thermoelastic analysis of the stress-focusing effect in a solid cylinder under rotationally asymmetrical instantaneous thermal loading

Summary  This paper investigates the stress-focusing effect in an infinitely long cylinder under rotationally asymmetrical instantaneous thermal loading on the basis of the generalized thermoelastic Lord–Shulman (L-S) and Green–Lindsay (G-L) theories. Combined forms of the governing equations of both theories are given in a cylindrical coordinate system. The two-dimensional generalized thermoelastic problems are solved by numerical inversion of Laplace transform. Calculations have been performed to find distributions of thermal stresses on the basis of the L-S theory. Stress-focusing phenomena under different heating conditions are presented. The effects of thermomechanical coupling and relaxation time on the stress-focusing phenomena as well as the singularity of stresses are discussed. Received 15 November 2000; accepted for publication 15 November 2001     

The crossover between linear and non-linear mechanical behaviour in polymer solutions as detected by Fourier-transform rheology

 The application of oscillatory shear strain leads, in the non-linear regime, to the appearance of higher harmonic contributions in the shear stress response. These contributions can be analyzed as spectra in Fourier space, with respect to different frequencies, amplitudes and phase angles. In this article, we present an application of this new characterization method to a solution of the linear homopolymer polyisobutylene. The degree of non-linear response during oscillatory shear is quantified using the normalized intensity of the third harmonic contribution. We were able to show experimentally on polyisobutylene that there is an immediate onset of the non-linear response even for very small shear strain amplitudes. Received: 21 June 1999/Accepted: 21 August 1999     

Quantitative rheological evaluation of phase inversion in two-phase polymer blends with cocontinuous morphology

 The present work is focused on the rheological properties of two-phase polymer blends in the phase inversion region. A large number of PS/PMMA- and PSAN/PMMA-blends has been investigated in order to establish a rheological criterion which allows the quantitative determination of the phase inversion concentration φ_PI by rheological means. Three rheological criteria based on the viscous and elastic blend properties such as maximum of dynamic viscosity η′, slope of G′, and maximum of G′ at a constant evaluation frequency have been tested. By correlating the rheological results to data from quantitative morphological analysis we could prove that the chosen rheological criteria are differently suitable for the determination of φ_PI. It has turned out that the G′ criterion is the most robust and most suitable one yielding an excellent correlation with morphological data. Based on these findings we propose a new simple equation for the prediction of φ_PI-values. Received: 14 March 2001 Accepted: 15 May 2001     

Temperature and stress analysis of an elastic circular cylinder in contact with heated rigid stamps

Summary  The present paper discusses a plane strain problem of transient thermoelasticity in a circular cylinder which is in partial contact with two heated rigid stamps, in the case where the coefficient of relative heat transfer on the contact surface of the cylinder is different from that on the traction-free surface. A finite difference method with respect to the time variable and Airy's thermal stress function is employed to analyze the temperature and thermoelastic fields. The problem is formulated in terms of two dual-series equations derived not only from the thermal boundary conditions but also from the mechanical boundary conditions. Since the radial, hoop and axial stresses have singularities at the end of the contact surface of the cylinder, the stress singularity coefficients are defined and then the relationship among these three coefficients is also obtained. Finally, numerical results are illustrated graphically. Received 3 March 2000; accepted for publication 12 July 2000     

The analysis of thermal stresses in thermopiezoelastic semi-infinite body with an edge crack

Summary  Thermopiezoelastic materials have recently attracted considerable attention because of their potential use in intelligent or smart structural systems. The governing equations of a thermopiezoelastic medium are more complex due to the intrinsic coupling effects that take place among mechanical, electrical and thermal fields. In this analysis, we deal with the problem of a crack in a semi-infinite, transversely isotropic, thermopiezoelastic material by means of potential functions and Fourier transforms under steady heat-flux loading conditions. The problem is reduced to a singular integral equation that is solved. The thermal stress intensity factor for a crack situated in a cadmium selenide material is calculated. Received 20 March 2001; accepted for publication 18 October 2001     

A Green's function approach to the deflection of a FGM plate under transient thermal loading

Summary  Green's function approach is adopted for analyzing the deflection and the transient temperature distribution of a plate made of functionally graded materials (FGMs). The governing equations for the deflection and the transient temperature are formulated into eigenvalue problems by using the eigenfunction expansion theory. Green's functions for solving the deflection and the transient temperature are obtained by using the Galerkin method and the laminate theory, respectively. The eigenfunctions of Green's function for the deflection are approximated in terms of a series of admissible functions that satisfy the homogeneous boundary conditions of the plate. The eigenfunctions of Green's function for the temperature are determined from the continuity conditions of the temperature and the heat flux at interfaces. Received 9 October 2000; accepted for publication 3 April 2001     

Timoshenko curved beam bending solutions in terms of Euler-Bernoulli solutions

Summary  This paper presents the exact relationships between the deflections and stress resultants of Timoshenko curved beams and that of the corresponding Euler-Bernoulli curved beams. The curved beams considered are of rectangular cross sections and constant radius of curvature. They may have any combinations of classical boundary conditions, and are subjected to any loading distribution that acts normal to the curved beam centreline. These relationships allow engineering designers to directly obtain the bending solutions of Timoshenko curved beams from the familiar Euler-Bernoulli solutions without having to perform the more complicated shear deformation analysis. Accepted for publication 26 July 1996     

Viscoelastic properties of pig kidney in shear, experimental results and modelling

 In this paper, the results from a series of rheological tests of fresh pig kidney have been reported. Using a standard strain-controlled rheometer, the oscillation strain sweep experiment showed a linear viscoelastic strain limit of the order of 0.2% strain. To determine the components of dynamic moduli in terms of frequency, shear oscillation tests were done at strain 0.2% using a stress-controlled rheometer. Shear stress relaxation tests were carried out with a fixed strain of 0.2% and 0.02 s rise time. The model we have developed uses a multi-mode upper convected Maxwell (UCM) model with variable viscosities and time constants, to which we have added a Mooney hyper-elastic response, both multiplied by a damping function. Different forms of damping functions that control the non-linearity of strain-stress profile have been tested. The model was fitted to our experimental data, and matched the entire test data reasonably well with a single set of parameters. Received: 5 May 2000 Accepted: 16 March 2001     

Exact solution of external tangential contact problem for a transversely isotropic elastic half-space

Summary  The following mixed boundary-value problem for a transversely isotropic elastic half-space is considered. Arbitrary tangential displacements are prescribed at the exterior of a circle, while the interior of the circle is free of tangential stress, and the normal stress vanishes all over the boundary. The governing integral equation is solved exactly, in closed form, and in terms of elementary functions. The method of continuation of solutions previously published by the author has been used here. Several examples are considered. No similar results has been reported before, even in the case of an isotropic body. Received 8 May 2000; accepted for publication 20 July 2000     

Particle size and boundary geometry effects on the bulk friction coefficient of sheared granular materials in the inertial regime

Glass beads of varying diameters (d=2,3,4$d=2,3,4$, and 5 mm) are used to measure the ratio of shear-to-normal stress, or bulk friction coefficient, generated inside an annular shear cell at high shearing rates. The effects of the particle size, the solids concentration, and the shear rate are explored. It is found that (1) for a given particle size, the magnitude of the bulk friction coefficient decreases with increasing solids concentration, (2) for a given solids concentration, the bulk friction coefficient decreases with increasing particle size, and (3) the bulk friction coefficient is independent of the shear rate except for cases with low solids concentration, where it decreases with increasing shear rate. The boundary geometry is found to affect bulk friction only for dilute (low solids concentration) flows involving small particles.     

Polydomain model predictions of liquid crystalline polymer orientation in mixed shear/extensional channel flows

 The Larson-Doi (LD) polydomain model is used to simulate orientation development along the centerline of slit-expansion and slit-contraction flows of liquid crystalline polymers (LCPs). Orientation is computed using the LD structural evolution equations, subject to an imposed velocity field that accounts for the spatial variation of both shear and extension rates characteristic of this class of flows. Computed axial distributions of orientation averaged through the sample thickness are qualitatively similar to birefringence and X-ray scattering measurements of molecular orientation in similar flows of lyotropic and thermotropic LCPs. In slit-expansion flows, the simulations predict a 90^∘ flip in orientation direction near the midplane due to transverse stretching in the expansion region. Far away from the midplane where shear gradients dominate, orientation remains primarily along the flow direction. Within the LD model, tumbling and flow aligning materials respond in a qualitatively similar manner to mixed shear and extension, although tumbling materials are systematically more susceptible to the effects of extension. Received: 22 October 1999/Accepted: 13 January 2000