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

High Mass Triple Systems: The Classical Cepheid Y Car

We have obtained an HST STIS ultraviolet high dispersion Echelle mode spectrum the binary companion of the double mode classical Cepheid Y Car. The velocity measured for the hot companion from this spectrum is very different from reasonable predictions for binary motion, implying that the companion is itself a short period binary. The measured velocity changed by 7 km/ s during the 4 days between two segments of the observation confirming this interpretation. We summarize "binary" Cepheids which are in fact members of triple system and find at least 44% are triples. The summary of information on Cepheids with orbits makes it likely that the fraction is under-estimated.Comment: accepted by A

The Search for Stellar Companions to Exoplanet Host Stars Using the CHARA Array

Most exoplanets have been discovered via radial velocity studies, which are inherently insensitive to orbital inclination. Interferometric observations will show evidence of a stellar companion if it sufficiently bright, regardless of the inclination. Using the CHARA Array, we observed 22 exoplanet host stars to search for stellar companions in low-inclination orbits that may be masquerading as planetary systems. While no definitive stellar companions were discovered, it was possible to rule out certain secondary spectral types for each exoplanet system observed by studying the errors in the diameter fit to calibrated visibilities and by searching for separated fringe packets.Comment: 26 pages, 5 tables, 8 figure

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

Existence of solutions for a higher order non-local equation appearing in crack dynamics

In this paper, we prove the existence of non-negative solutions for a non-local higher order degenerate parabolic equation arising in the modeling of hydraulic fractures. The equation is similar to the well-known thin film equation, but the Laplace operator is replaced by a Dirichlet-to-Neumann operator, corresponding to the square root of the Laplace operator on a bounded domain with Neumann boundary conditions (which can also be defined using the periodic Hilbert transform). In our study, we have to deal with the usual difficulty associated to higher order equations (e.g. lack of maximum principle). However, there are important differences with, for instance, the thin film equation: First, our equation is nonlocal; Also the natural energy estimate is not as good as in the case of the thin film equation, and does not yields, for instance, boundedness and continuity of the solutions (our case is critical in dimension $1$ in that respect)

Formability and Damage in Electromagnetically Formed AA5754 and AA6111

This paper presents the results of experiments carried out to determine the formability of AA5754 and AA6111 using electromagnetic forming (EMF), and the effect of the tool/sheet interaction on damage evolution and failure. The experiments consisted of forming 1mm sheets into conical dies of 40° and 45° side angle, using a spiral coil. The experiments showed that both alloys could successfully be formed into the 40?? die, with strains above the conventional forming limit diagram (FLD) of both alloys. Forming into the higher 45° cone resulted in failure for both materials. Metallographic analysis indicated that damage is suppressed during the forming process. Micrographs of the necked and fractured areas of the part show evidence that the materials do not fail in pure ductile fracture, but rather in what could be a combination of plastic collapse, ductile fracture and shear band fracture. The failure modes are different for each material; with the AA5754 parts failing by necking and fracture, with significant thinning at the fracture tip. The AA6111 exhibited a saw tooth pattern fractures, a crosshatch pattern of shear bands in the lower half of the part, and tears in the area close to the tip. Both areas showed evidence of shear fracture. This experimental study indicates that there is increased formability for AA5754 and AA6111 when these alloys are formed using EMF. A major factor in this increase in formability is the reduction in damage caused by the tool/sheet interaction

A kinetic formulation for multidimensional scalar conservation laws with boundary conditions and applications

International audienceWe state a kinetic formulation of weak entropy solutions of a general multidimensional scalar conservation law with initial and boundary conditions. We first associate with any weak entropy solution a entropy defect measure; the analysis of this measure at the boundary of the domain relies on the study of weak entropy sub and supersolutions and implies the introduction of the notion of sided boundary defect measures. As a first application, we prove that any weak entropy subsolution of the initial-boundary value problem is bounded above by any weak entropy supersolution (Comparison Theorem). We next study a BGK-like kinetic model that approximates the scalar conservation law. We prove that such a model converges by adapting the proof of the Comparison Theorem

The OSACA Database and a Kinematic Analysis of Stars in the Solar Neighborhood

We transformed radial velocities compiled from more than 1400 published sources, including the Geneva--Copenhagen survey of the solar neighborhood (CORAVEL-CfA), into a uniform system based on the radial velocities of 854 standard stars in our list. This enabled us to calculate the average weighted radial velocities for more than 25~000 HIPPARCOS stars located in the local Galactic spiral arm (Orion arm) with a median error of +-1 km/s. We use these radial velocities together with the stars' coordinates, parallaxes, and proper motions to determine their Galactic coordinates and space velocities. These quantities, along with other parameters of the stars, are available from the continuously updated Orion Spiral Arm CAtalogue (OSACA) and the associated database. We perform a kinematic analysis of the stars by applying an Ogorodnikov-Milne model to the OSACA data. The kinematics of the nearest single and multiple main-sequence stars differ substantially. We used distant (r\approx 0.2 kpc) stars of mixed spectral composition to estimate the angular velocity of the Galactic rotation -25.7+-1.2 km/s/kpc, and the vertex deviation,l=13+-2 degrees, and detect a negative K effect. This negative K effect is most conspicuous in the motion of A0-A5 giants, and is equal to K=-13.1+-2.0 km/s/kpc.Comment: 16 pages, 8 figure

Structure and Evolution of Nearby Stars with Planets. I. Short-Period Systems

Using the Yale stellar evolution code, we have calculated theoretical models for nearby stars with planetary-mass companions in short-period nearly circular orbits: 51 Pegasi, Tau Bootis, Upsilon Andromedae, Rho Cancri, and Rho Coronae Borealis. We present tables listing key stellar parameters such as mass, radius, age, and size of the convective envelope as a function of the observable parameters (luminosity, effective temperature, and metallicity), as well as the unknown helium fraction. For each star we construct best models based on recently published spectroscopic data and the present understanding of galactic chemical evolution. We discuss our results in the context of planet formation theory, and, in particular, tidal dissipation effects and stellar metallicity enhancements.Comment: 48 pages including 13 tables and 5 figures, to appear in Ap