Coupled analysis of material flow and die deflection in direct aluminum extrusion

The design of extrusion dies depends on the experience of the designer. After the die has\ud been manufactured, it is tested during an extrusion trial and machined several times until it works\ud properly. The die is designed by a trial and error method which is an expensive process in terms\ud of time and the amount of scrap. In order to decrease the time and the amount of scrap, research is\ud going on to replace the trial pressing with finite element simulations. The goal of these simulations\ud is to predict the material flow through the die. In these simulations, it is required to calculate the\ud material flow and the tool deformation simultaneously. Solving the system of equations concerning\ud the material flow and the tool deformation becomes more difficult with increasing the complexity\ud of the die. For example the total number of degrees of freedom can reach a value of 500,000 for\ud a flat die. Therefore, actions must be taken to solve the material flow and the tool deformation\ud simultaneously and faster. This paper describes the calculation of a flat die deformation used in the\ud production of a U-shape profile with a coupled method. In this calculation an Arbitrary Lagrangian\ud Eulerian and Updated Lagrangian formulation are applied for the aluminum and the tool finite\ud element models respectively. In addition, for decreasing the total number of degrees of freedom,\ud the stiffness matrix of the tool is condensed to the contact nodes between the aluminum and the tool\ud finite element models. Finally, the numerical results are compared with experiment results in terms\ud of extrusion force and the angular deflection of the tongue

Measuring the Deformation of a Flat Die by Applying a Laser Beam on a Reflecting Surface

The design of extrusion dies depends on the experience of the designer. After the die has been manufactured, it is tested during an extrusion process and machined several times until it works properly. The die is designed by a trial and error method which is expensive interms of time consumption and the amount of scrap. Research is going on to replace the trial pressing with finite element simulations that concentrate on material and tool analysis. In order to validate the tool simulations, an experiment is required for measuring the deformation of the die. Measuring the deformation of the die is faced with two main obstacles: high temperature and little free space. To overcome these obstacles a method is tried, which works by applying a laser beam on a reflecting surface. This cheap method is simple, robust and gives good results. This paper describes measuring the deformation of a flat die used to extrude a single U shape profile. In addition, finite element calculation of the die is performed. Finally, a comparison is performed between experimental and numerical results

Boundary conditions applied on bearing corner in direct aluminum extrusion

Finite element analysis in aluminum extrusion is faced by several problems such as number of degrees of freedom, calculation time, large deformation and flow conservation. The problem of large deformation is overcome by applying the Eulerian formulation. But the problems concerning number of degrees of freedom, calculation time can be overcome by the model simplification especially at the bearing corner. On the one hand, detailed modeling of the bearing corner will increase the complexity of the analysis. On the other hand, simplified modeling of the bearing corner will face problems such as locking of the corner node and flow conservation. Therefore, boundary conditions will be applied at the corner node in order to solve the problem of its locking and to satisfy the aluminum flow conservation. These boundary conditions include normal and constraint equation. This paper focuses on the calculation of the normal with different elements such as plane strain, axisymmetric and tetrahedron elements. The constraint equation at different positions of the corner node is determined for a plane strain element only. The extrusion force and average exit velocity are investigated and compared with the triple node method and reference model. Where, in the reference model the contact boundary condition is applied between the rigid die and aluminum. Eulerian formulation is applied in finite element analysis unless in the reference model the Arbitrary Lagrangian Eulerian formulation is applied

Comment on "Quantum Monte Carlo Evidence for Superconductivity in the Three-Band Hubbard Model in Two Dimensions"

In a recent Letter, Kuroki and Aoki [Phys. Rev. Lett. 76, 440 (1996)] presented quantum Monte-Carlo (QMC) results for pairing correlations in the three-band Hubbard model, which describes the Cu-d_{x^2-y^2} and O-p_{x,y} orbitals present in the CuO_2 planes of high-T_c materials. In this comment we argue that (i) the used parameter set is not appropriate for the description of high-T_c materials since it does not satisfy the minimal requirement of a charge-transfer gap at half-filling, and (ii) the observed increase in the d_{x^2-y^2} channel is dominantly produced by the pair-field correlations without the vertex part. Hence, the claim of evidence of ODLRO is not justified.Comment: 1 page latex and 2 eps-figures, uses epsfig, submitted to PR

Dynamic Exponent of t-J and t-J-W Model

Drude weight of optical conductivity is calculated at zero temperature by exact diagonalization for the two-dimensional t-J model with the two-particle term, $W$. For the ordinary t-J model with $W$=0, the scaling of the Drude weight $D \propto \delta^2$ for small doping concentration $\delta$ is obtained, which indicates anomalous dynamic exponent $z$=4 of the Mott transition. When $W$ is switched on, the dynamic exponent recovers its conventional value $z$=2. This corresponds to an incoherent-to-coherent transition associated with the switching of the two-particle transfer.Comment: LaTeX, JPSJ-style, 4 pages, 5 eps files, to appear in J. Phys. Soc. Jpn. vol.67, No.6 (1998

Charge and Spin Structures of a dx2−y2d_{x^2 - y^2} Superconductor in the Proximity of an Antiferromagnetic Mott Insulator

To the Hubbard model on a square lattice we add an interaction, $W$, which depends upon the square of a near-neighbor hopping. We use zero temperature quantum Monte Carlo simulations on lattice sizes up to $16 \times 16$, to show that at half-filling and constant value of the Hubbard repulsion, the interaction $W$ triggers a quantum transition between an antiferromagnetic Mott insulator and a $d_{x^2 -y^2}$ superconductor. With a combination of finite temperature quantum Monte Carlo simulations and the Maximum Entropy method, we study spin and charge degrees of freedom in the superconducting state. We give numerical evidence for the occurrence of a finite temperature Kosterlitz-Thouless transition to the $d_{x^2 -y^2}$ superconducting state. Above and below the Kosterlitz-Thouless transition temperature, $T_{KT}$, we compute the one-electron density of states, $N(\omega)$, the spin relaxation rate $1/T_1$, as well as the imaginary and real part of the spin susceptibility $\chi(\vec{q},\omega)$. The spin dynamics are characterized by the vanishing of $1/T_1$ and divergence of $Re \chi(\vec{q} = (\pi,\pi), \omega = 0)$ in the low temperature limit. As $T_{KT}$ is approached $N(\omega)$ develops a pseudo-gap feature and below $T_{KT}$ $Im \chi(\vec{q} = (\pi,\pi), \omega)$ shows a peak at finite frequency.Comment: 46 pages (latex) including 14 figures in encapsulated postscript format. Submitted for publication in Phys. Rev.

Doping induced metal-insulator transition in two-dimensional Hubbard, t−Ut-U, and extended Hubbard, t−U−Wt-U-W, models

We show numerically that the nature of the doping induced metal-insulator transition in the two-dimensional Hubbard model is radically altered by the inclusion of a term, $W$, which depends upon a square of a single-particle nearest-neighbor hopping. This result is reached by computing the localization length, $\xi_l$, in the insulating state. At finite values of $W$ we find results consistent with $\xi_l \sim | \mu - \mu_c|^{- 1/2}$ where $\mu_c$ is the critical chemical potential. In contrast, $\xi_l \sim | \mu - \mu_c|^{-1/4}$ for the Hubbard model. At finite values of $W$, the presented numerical results imply that doping the antiferromagnetic Mott insulator leads to a $d_{x^2 - y ^2}$ superconductor.Comment: 19 pages (latex) including 7 figures in encapsulated postscript format. Submitted for publication in Phys. Rev.