Energy release rates in a constrained epoxy disc with Hookean and Mooney–Rivlin materials

Assuming that the disc material can be modeled either as Mooney–Rivlin or as Hookean and the steel ring enclosing the disc as Hookean, the energy release rates as a function of the crack length are evaluated and compared. Two loadings are considered––one in which the surface of the star shape hole in the disc is loaded by a uniform pressure and the other in which the temperature of the composite body is uniformly raised. It is found that the linear and the nonlinear analyses give qualitatively similar results for the two loadings. For each load, the energy release rate increases with an increase in the starter crack length, reaches a maximum value and then decreases gradually.     

A model of debonding instability for solid propellant rocket motor: Part II — Unequal longitudinal and transverse stress rate

Considered in Part I was the debonding instability of a three-layered composite system made of steel, adhesive and rubber which models the situation in a solid-fuel rocket motor. Under the condition of a uniform stress rate of 0.75 ksi/s applied to the longitudinal and transverse direction, severe inhomogeneity of the material response were found in regions next to the adhesive/rubber interface. This led to the prediction of a macrocrack about 5 × 10⁻³ in. after an elapsed time of one second and sudden fracture over a length of 1.88 in. at eight seconds after loading.This is Part II of the work that examines the influence of load transients on interface failure. As unequal stress rate state is assumed where loading in the transverse direction is removed causing a more severe disturbance in the longitudinal direction even though the same stress rate of 0.75 ksi/s is maintained. A slightly bent crack of the order of 10⁻³ in. is predicted to initiate near the adhesive/rubber interface; it led to the onset of fracture over a length of 1.60 in. at four seconds. Onset of instability is predicted to occur at a much earlier state.     

An investigation of interior ballistics ignition phase

An axisymmetric viscous two-phase model is presented which describes the transient combustion of granular propellants during the ignition phase of a ballistic charge. Details of the model are presented along with computational results for a low-pressure ballistic simulator. Predicted pressure time evolutions are compared with experimental data of a real test-firing in which an unexpected pressure excursion occurred. Gun propellant breakup effects, due to bed compaction, are taken into consideration to explain the discrepancies between the numerical and experimental results. Finally, a discussion is presented of the mechanisms by which the behavior of pressure waves can be strongly influenced and thus controlled by the manner in which the propelling charge is ignited.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

A theory of finite elastic consolidation

Presented in this paper is a general theory describing the consolidation of a porous elastic soil. The formulation allows for the occurrence of finite geometry changes and finite elastic strains during the consolidation process. The governing equations have been cast in a rate form and the laws which determine deformation and pore fluid flow, i.e. Hooke's law and Darcy's law, are presented in a frame indifferent manner. A numerical technique is described that provides an approximate solution to the governing equations. The theory and the solution technique are illustrated by several examples of practical interest.     

An analytical prediction of sliding motions along discontinuous boundary in non-smooth dynamical systems

This paper presents a method for the analytical prediction of sliding motions along discontinuous boundaries in non-smooth dynamical systems. The methodology is demonstrated through investigation of a periodically forced linear oscillator with dry friction. The switching conditions for sliding motions in non-smooth dynamical systems are given. The generic mappings for the friction-induced oscillator are introduced. From the generic mappings, the corresponding criteria for the sliding motions are presented through the force product conditions. The analytical prediction of the onset and vanishing of the sliding motions is illustrated. Finally, numerical simulations of sliding motions are carried out to verify the analytical prediction. This analytical prediction provides an accurate prediction of sliding motions in non-smooth dynamical systems. The switching conditions developed in this paper are expressed by the total force of the oscillator, and the nonlinearity and linearity of the spring and viscous damping forces in the oscillator cannot change such switching conditions. Therefore, the achieved force criteria can be applied to the other dynamical systems with nonlinear friction forces processing a C ⁰-discontinuity.     

Application of holographic interferometry to a study of wave propagation in rock

Holographic interferometry was utilized to determine the three orthogonal components of displacement in elastic surface waves. A pulsed ruby laser was used as the light source and techniques to improve its coherence properties are described. Procedures for the formation and reconstruction of the hologram, fringe interpretation, and data reduction and presentation are detailed. The elastic-wave velocities and material constants for pink westerly granite were obtained. Solutions for an explosively generated Rayleigh wave in a half space and its reflection from a free edge are presented.     

Torsion pendula with electromagnetic drive and detection system for measuring the complex shear modulus of liquids in the frequency range 80–2500 Hz

An apparatus for the measurement of liquid complex shear viscosity in the frequency range 80–2500 Hz, with the use of a torsion pendulum operating in forced oscillation, is described. The drive and detection system consists of a magnet inside the pendulum, two excitation and two measuring coils. The determination of the complex shear viscosity is based on the measurement of the resonance frequency and the damping of the torsion pendulum.The feasibility of this method is demonstrated with a number of Newtonian liquids in the viscosity range 0.3 to 60 m Pa s. Results for a viscoelastic polymer solution are presented. A comparison is made with other apparatus working in the same frequency range. a coil height - A apparatus constant - B magnetic induction - C ₁,C ₂ apparatus constants - d diameter torsion rod - D pendulum damping - E apparatus constant - F ₀ top frequency - G shear modulus torsion rod - G ^* =G + iG complex shear modulus - h length torsion rod - H transfer function - i - I moment of inertia - J ₀ excitation-current amplitude - J _exc excitation current - K torsion spring constant - l length pendulum mass - M torque - n number of coil turns - p dipole moment - Q = ₀/ mechanical quality - r radius pendulum mass - R Re {Z} - t time - T temperature - U induction voltage - U ₀ induction-voltage amplitude - x distance - X Im {Z} - Z = R + iX liquid impedance - Z _cyl characteristic cylindrical impedance - Z _pl characteristic plane impedance - angle - _M coefficient of linear expansion of the pendulum mass - _R coefficient of linear expansion of the torsion rod - rate of shear - penetration depth - steady-state viscosity - _s solvent viscosity - angular displacement - ₀ angular-displacement amplitude - µ ₀ =4 10^–7 Vs/Am - density - phase angle - angular frequency - ₀ top angular frequency - band-width     

Analysis of buoyancy-aided convection heat transfer from a horizontal cylinder in a vertical duct at low Reynolds number

This paper reports a numerical study on buoyancy-aided steady convection heat transfer from a horizontal cylinder situated in a vertical adiabatic duct. Numerical results have been generated forH ₁/D=2.5, 4, 8,H/D=8, 16, 24,S/D=2, 4, 6, 20Re60, andRi up to 4. The placing of a horizontal cylinder in a vertical duct of smaller width results in significantly enhanced pure forced convection due to the blockage effect, but degrades appreciably the extent of buoyancy-aided enhancement in the heat transfer rate. Nevertheless, the presence of a vertical duct leads to an overall enhancement of mixed convection heat transfer coefficient relative to that without the confining duct. Moreover, the average Nusselt number is rather insensitive to the variation of either the position of the cylinder in the duct or the duct height in the investigated ranges of these geometric parameters.Dieser Artikel beschreibt eine numerische Studie über auftriebsunterstützte konvektive Wärmeübertragung von einem horizontalen Zylinder der in einem vertikalen adiabaten Kanal positioniert ist. Die numerischen Ergebnisse sind fürH ₁/D=2, 5, 4, 8,H/D=8, 16, 24,S/D=2, 4, 6 sowie 20Re60 undRi bis 4 berechnet worden. Die Anordnung des horizontalen Zylinders in einem schmaleren vertikalen Kanal führt auf Grund des Blockierungs-effektes zu einem deutlichen Anstieg der reinen Zwangskonvektion. Aber sie verschlechtert deutlich den Betrag der auftriebsbedingten Steigerung in der Wärmeübergangsrate. Trotzdem führt die Anwesenheit des vertikalen Kanals insgesamt zu einer Steigerung des Wärmeübergangskoeffizienten bei Mischkonvektion im Vergleich zur Abwesenheit des begrenzenden Kanals. Des weiteren ist die durchschnittliche Nusseltzahl von der Variation der Zylinderposition im Kanal oder der Kanalhöhe abhängig.