Development of an Interrupted Pulse Expanding Ring Test

An interrupted pulse electromagnetic (EM) expanding ring test is being developed at the University of Waterloo to study the high rate behaviour of sheet metals. In a classic EM expanding ring test, a ring is expanded radially using the forces induced on the ring by a high frequency high intensity current flowing in a nearby coil. If the driving force and the acceleration of the ring are known, then the stress-strain history of the ring can be determined. Coil currents are typically generated by large capacitor banks that produce a current discharge in the shape of a damped sinusoid. To properly determine the stress of the ring, the forces induced on the ring by the current pulse must be known, which is difficult to do in practice. The approach taken in this work is to interrupt the current by means of an exploding wire switch to eliminate the Lorentz forces and achieve a free flight condition, where the stress can be determined using only the measured velocity and density of the ring. The velocity of the rings was measured using a photon Doppler velocimeter (PDV). With this technique significant periods of free-flight were obtained, with the corresponding stressstrain data. Results for 1.5 mm sheet of AA 5182-O are presented

Contributing Factors to the Increased Formability Observed in Electromagnetically Formed Aluminum Alloy Sheet

This paper summarizes the results of an experimental and numerical program carried out to study the formability of aluminum alloy sheet formed using electromagnetic forming (EMF). Free-formed and conical samples of AA5754 aluminum alloy sheet were studied. The experiments showed significant increases in formability for the conical samples, but no significant increase for the free-formed parts. It was found that relatively little damage growth occurred and that the failure modes of the materials changed from those observed in quasi-static forming to those observed in high hydrostatic stress environments. Numerical simulations were performed using the explicit finite element code LS-DYNA with an analytical EM force distribution. The numerical models revealed that a complex stress state is generated when the sheet interacts with the tool, which is characterized by high hydrostatic stresses that create a stress state favourable to damage suppression increasing ductility. Shear stresses and strains are also produced at impact with the die which help the material achieve additional deformation. The predicted peak strain rates for the free formed parts were on the order of 1000 s^(-1) and for the conical parts the rates are on the order of 10,000 s^(-1). Although aluminum is typically considered to be strain-rate insensitive, the strain rates predicted could be playing a role in the increased formability. The predicted strain paths for the conical samples were highly non-linear. The results from this study indicate that there is an increase in formability for AA5754 when the alloy is formed into a die using EMF. This increase in formability is due to a combination of high hydrostatic stresses, shear stresses, high strain rates, and non-linear strain paths

Contribution to the search for binaries among Am stars - VII. Orbital elements of seven new spectroscopic binaries, implications on tidal effects

International audienceWe present the results of a radial-velocity study of seven Am stars (HD 3970, 35035, 93946, 151746, 153286, 204751 and 224002) observed at the Observatoire de Haute-Provence (OHP) and the Cambridge Observatories with CORAVEL instruments. We find that these systems are single-lined spectroscopic binaries whose orbital elements are determined for the first time. Among this sample, HD 35035 and 153286 have long periods, with P = 2.8 and 9.5yr, respectively, which is rather unusual for Am stars. Four systems have orbits with large eccentricities (with e >= 0.4). Physical parameters are inferred from this study for the primaries of those systems. We then investigate the influence of tidal interaction, which has already led to the synchronism of the primaries and/or to the circularization of the orbits of some systems belonging to this sample. We extend this study to the list of 33 objects studied in this series of papers and derive values of the critical fractional radii r = R/a for circularization and synchronization of Am-type binaries. We find that the stars with r >~ 0.15 are orbiting on circular orbits and that synchronism is likely for all components with r >~ 0.20

Effects of Force Distribution and Rebound on Electromagnetically Formed Sheet Metal

Electromagnetic forming (EMF) is a high speed forming process that has been shown to increase the formability of aluminum alloys under certain conditions. Many authors have reported significant increases in formability; however, there is as of yet no complete understanding of the process. Obtaining a gain in formability is not the only factor that must be considered when studying EMF. The process rapidly generates significant forces which lead to the deformation of the material at very high rates. The applied forces depend on the shape of the electromagnetic coil used, which leads to force distributions that may not be ideal for forming a particular part. Once the sheet is accelerated it will travel at high speeds until it impacts the die. This high speed impact results in the sheet rebounding from the die. Both the force distribution and the rebound affect the final shape of the part. This paper presents the results of experimental and numerical study carried out to determine the effect of the force distribution and the rebound on samples of conical and "v-channel" geometry. It was found that both sample geometries are affected by the force distribution and the rebound, with the v-channel samples being considerably more affected. The results indicate that these effects must be carefully considered when EMF processes are designed

Role of beam propagation in Goos-H\"{a}nchen and Imbert-Fedorov shifts

We derive the polarization-dependent displacements parallel and perpendicular to the plane of incidence, for a Gaussian light beam reflected from a planar interface, taking into account the propagation of the beam. Using a classical-optics formalism we show that beam propagation may greatly affect both Goos-H\"{a}nchen and Imbert-Fedorov shifts when the incident beam is focussed.Comment: 3 pages, 1 figure, submitted to Opt. Let

On the Numerical Approximations of an Optimal Correction Problem

The numerical solution of an optimal correction problem for a damped random linear oscillator is studied. A numerical algorithm for the discretized system of the associated dynamic programming equation is given. To initiate the computation, we adopt a numerical scheme derived from the deterministic version of the problem. Next, a correction-type algorithm based on a discrete maximum principle is introduced to ensure the convergence of the iteration procedure

Repeated games for eikonal equations, integral curvature flows and non-linear parabolic integro-differential equations

The main purpose of this paper is to approximate several non-local evolution equations by zero-sum repeated games in the spirit of the previous works of Kohn and the second author (2006 and 2009): general fully non-linear parabolic integro-differential equations on the one hand, and the integral curvature flow of an interface (Imbert, 2008) on the other hand. In order to do so, we start by constructing such a game for eikonal equations whose speed has a non-constant sign. This provides a (discrete) deterministic control interpretation of these evolution equations. In all our games, two players choose positions successively, and their final payoff is determined by their positions and additional parameters of choice. Because of the non-locality of the problems approximated, by contrast with local problems, their choices have to "collect" information far from their current position. For integral curvature flows, players choose hypersurfaces in the whole space and positions on these hypersurfaces. For parabolic integro-differential equations, players choose smooth functions on the whole space