Automated optimization of polymer extrusion dies using finite element analysis

An extrusion die is used to continuously produce parts with a constant cross section; such as sheets, pipes, tire components and more complex shapes such as window seals. The die is fed by a screw extruder when polymers are used. The extruder melts, mixes and pressures the material by the rotation of either a single or double screw. The polymer can then be continuously forced through the die producing a long part in the shape of the die outlet. The extruded section is then cut to the desired length. Generally, the primary target of a well designed die is to produce a uniform outlet velocity without excessively raising the pressure required to extrude the polymer through the die. Other properties such as temperature uniformity and residence time are also important but are not directly considered in this work. Designing dies for optimal outlet velocity variation using simple analytical equations are feasible for basic die geometries or simple channels. Due to the complexity of die geometry and of polymer material properties design of complex dies by analytical methods is difficult. For complex dies iterative methods must be used to optimize dies. An automated iterative method is desired for die optimization. To automate the design and optimization of an extrusion die two issues must be dealt with. The first is how to generate a new mesh for each iteration. In this work, this is approached by modifying a Parasolid file that describes a CAD part. This file is then used in a commercial meshing software. Skewing the initial mesh to produce a new geometry was also employed as a second option. The second issue is an optimization problem with the presence of noise stemming from variations in the mesh and cumulative truncation errors. In this work a simplex method and a modified trust region method were employed for automated optimization of die geometries. For the trust region a discreet derivative and a BFGS Hessian approximation were used. To deal with the noise in the function the trust region method was modified to automatically adjust the discreet derivative step size and the trust region based on changes in noise and function contour. Generally uniformity of velocity at exit of the extrusion die can be improved by increasing resistance across the die but this is limited by the pressure capabilities of the extruder. In optimization, a penalty factor that increases exponentially from the pressure limit is applied. This penalty can be applied in two different ways; the first only to the designs which exceed the pressure limit, the second to both designs above and below the pressure limit. Both of these methods were tested and compared in this work.

Surface quality of profile extrusion dies manufactured by Selective Laser Melting

The design of plastics profile extrusion dies becomes increasingly more complex so that conventional manufacture processes reach their limit in the die manufacture. A feasible manufacture of arbitrarily designed dies is only possible by additive manufacturing. An especially promising process is hereby the Selective Laser Melting with which metal parts with series identical mechanical properties can be produced without the need for part specific tooling or downstream sintering processes. Disadvantegeous is, however, the relatively rough surface of additively manufactured parts. Against this background, the manufacturing of an profile extrusion die by Selective Laser Melting and the plastics profile surface quality, that can be achieved with such dies, is investigated. For this purpose, profiles are extruded both with an additively manufactured die and a conventionally milled sample of the same die geometry. In case of the additively manufactured die a concept for the surface finishing of the flow channel is required, which can be applied to arbitrarily shaped geometries. Therefore, two different reworking processes are applied only to the die land of the flow channel. The comparison of the surface roughnesses shows that the additively manufactured die with a polished die land delivers the same surface quality as the conventional die.

Analyse de groupe d’un modèle de la plasticité idéale planaire et sur les solutions en termes d’invariants de Riemann pour les systèmes quasilinéaires du premier ordre

Les objets d’étude de cette thèse sont les systèmes d’équations quasilinéaires du premier ordre. Dans une première partie, on fait une analyse du point de vue du groupe de Lie classique des symétries ponctuelles d’un modèle de la plasticité idéale. Les écoulements planaires dans les cas stationnaire et non-stationnaire sont étudiés. Deux nouveaux champs de vecteurs ont été obtenus, complétant ainsi l’algèbre de Lie du cas stationnaire dont les sous-algèbres sont classifiées en classes de conjugaison sous l’action du groupe. Dans le cas non-stationnaire, une classification des algèbres de Lie admissibles selon la force choisie est effectuée. Pour chaque type de force, les champs de vecteurs sont présentés. L’algèbre ayant la dimension la plus élevée possible a été obtenues en considérant les forces monogéniques et elle a été classifiée en classes de conjugaison. La méthode de réduction par symétrie est appliquée pour obtenir des solutions explicites et implicites de plusieurs types parmi lesquelles certaines s’expriment en termes d’une ou deux fonctions arbitraires d’une variable et d’autres en termes de fonctions elliptiques de Jacobi. Plusieurs solutions sont interprétées physiquement pour en déduire la forme de filières d’extrusion réalisables. Dans la seconde partie, on s’intéresse aux solutions s’exprimant en fonction d’invariants de Riemann pour les systèmes quasilinéaires du premier ordre. La méthode des caractéristiques généralisées ainsi qu’une méthode basée sur les symétries conditionnelles pour les invariants de Riemann sont étendues pour être applicables à des systèmes dans leurs régions elliptiques. Leur applicabilité est démontrée par des exemples de la plasticité idéale non-stationnaire pour un flot irrotationnel ainsi que les équations de la mécanique des fluides. Une nouvelle approche basée sur l’introduction de matrices de rotation satisfaisant certaines conditions algébriques est développée. Elle est applicable directement à des systèmes non-homogènes et non-autonomes sans avoir besoin de transformations préalables. Son efficacité est illustrée par des exemples comprenant un système qui régit l’interaction non-linéaire d’ondes et de particules. La solution générale est construite de façon explicite.

Flow of metal in constrained plane-strain extrusion forging- Part II

With many innovations in process technology, forging is establishing itself as a precision manufacturing process: as forging is used to produce complex shapes in difficult materials, it requires dies of complex configuration of high strength and of wear-resistant materials. Extensive research and development work is being undertaken, internationally, to analyse the stresses in forging dies and the flow of material in forged components. Identification of the location, size and shape of dead-metal zones is required for component design. Further, knowledge of the strain distribution in the flowing metal indicates the degree to which the component is being work hardened. Such information is helpful in the selection of process parameters such as dimensional allowances and interface lubrication, as well as in the determination of post-forging operations such as heat treatment and machining. In the presently reported work the effect of aperture width and initial specimen height on the strain distribution in the plane-strain extrusion forging of machined lead billets is observed: the distortion of grids inscribed on the face of the specimen gives the strain distribution. The stress-equilibrium approach is used to optimise a model of flow in extrusion forging, which model is found to be effective in estimating the size of the dead-metal zone. The work carried out so far indicates that the methodology of using the stress-equilibrium approach to develop models of flow in closed-die forging can be a useful tool in component, process and die design.

The extrusion of continuous lengths of YBa2Cu3O7-x wire using hydroxypropyl methylcellulose

Wires of YBa2Cu3O7-x were fabricated by extrusion using a hydroxypropyl methylcellulose (HPMC) binder. As little as 2 wt.% binder was added to an oxide prepared by a novel co-precipitation process, to produce a plastic mass which readily gave continuous extrusion of long lengths of wire in a reproducible fashion. Critical temperatures of 92K were obtained for wires given optimum high-temperature heat treatments. Critical current densities greater than 1000 A cm-1 were measured at 77.3K using heat treatments at around 910°C for 10h. These transport critical current densities, measured on centimeter-long wires, were obtained with microstructures showing a relatively dense and uniform distribution of randomly oriented, small YBa2Cu3O7-x grains. © 1993.

Sonochemical nanoplungers : crystalline gold nanowires by cavitational extrusion through nanoporous alumina

Rapid, simple, catalyst-free, room-temperature sonochemical fabrication of long (up to 30 mm), ultra-thin (about 20 nm), crystalline gold nanowires on nanoporous anodic alumina membranes is reported. It is demonstrated that the nanowires nucleate and grow inside the nanosized pores and then form a dense network on the bottom side of the membrane. A growth mechanism is proposed based on the formation of through channels in the Al2O3 membrane by sonochemical etching, followed by nanowire nucleation in the channels and their further extrusion out of the pores by acoustic cavitation. This process can be used for the fabrication of metal nanowires with highly controllable diameter and density, suitable for numerous applications such as nanoelectronic, nanofluidic, and optoelectronic components and devices.

Validation of processing maps for 304L stainless steel using hot forging, rolling and extrusion

The development of a microstructure in 304L stainless steel during industrial hot-forming operations, including press forging (mean strain rate of 0.15 s(-1)), rolling/extrusion (2-5 s(-1)), and hammer forging (100 s(-1)) at different temperatures in the range 600-1200 degrees C, was studied with a view to validating the predictions of the processing map. The results have shown that excellent correlation exists between the regimes exhibited by the map and the product microstructures. 304L stainless steel exhibits instability bands when hammer forged at temperatures below 1100 degrees C, rolled/extruded below 1000 degrees C, or press forged below 800 degrees C. All of these conditions must be avoided in mechanical processing of the material. On the other hand, ideally, the material may be rolled, extruded, or press forged at 1200 degrees C to obtain a defect-free microstructure.

Flow of metal into the flash gap in the last stages of a plane-strain closed-die forging operation

In closed-die forging the flash geometry should be such as to ensure that the cavity is completely filled just as the two dies come into contact at the parting plane. If metal is caused to extrude through the flash gap as the dies approach the point of contact — a practice generally resorted to as a means of ensuring complete filling — dies are unnecessarily stressed in a high-stress regime (as the flash is quite thin and possibly cooled by then), which reduces the die life and unnecessarily increases the energy requirement of the operation. It is therefore necessary to carefully determine the dimensions of the flash land and flash thickness — the two parameters, apart from friction at the land, which control the lateral flow. The dimensions should be such that the flow into the longitudinal cavity is controlled throughout the operation, ensuring complete filling just as the dies touch at the parting plane. The design of the flash must be related to the shape and size of the forging cavity as the control of flow has to be exercised throughout the operation: it is possible to do this if the mechanics of how the lateral extrusion into the flash takes place is understood for specific cavity shapes and sizes. The work reported here is part of an ongoing programme investigating flow in closed-die forging. A simple closed shape (no longitudinal flow) which may correspond to the last stages of a real forging operation is analysed using the stress equilibrium approach. Metal from the cavity (flange) flows into the flash by shearing in the cavity in one of the three modes considered here: for a given cavity the mode with the least energy requirement is assumed to be the most realistic. On this basis a map has been developed which, given the depth and width of the cavity as well as the flash thickness, will tell the designer of the most likely mode (of the three modes considered) in which metal in the cavity will shear and then flow into the flash gap. The results of limited set of experiments, reported herein, validate this method of selecting the optimum model of flow into the flash gap.

Temperature characteristics of the billet and the dies in a small batch forging production

The work reported herein is part of an on-going programme to develop a computer code which, given the geometrical, process and material parameters of the forging operation, is able to predict the die and the billet cooling/heating characteristics in forging production. The code has been experimentally validated earlier for a single forging cycle and is now validated for a small batch production. To facilitate a step-by-step development of the code, the billet deformation has so far been limited to its surface layers, a situation akin to coining. The code has been used here to study the effects of die preheat-temperature, machine speed and rate of deformation the cooling/heating of the billet and the dies over a small batch of 150 forgings. The study shows: that there is a pre-heat temperature at which the billet temperature changes little from one forging to the next; that beyond a particular number of forgings, the machine speed ceases to have any pronounced influence on the temperature characteristics of the billet; and that increasing the rate of deformation reduces the heat loss from the billet and gives the billet a stable temperature profile with respect to the number of forgings. The code, which is simple to use, is being extended to bulk-deformation problems. Given a practical range of possible machine, billet and process specifics, the code should be able to arrive at a combination of these parameters which will give the best thermal characteristics of the die-billet system. The code is also envisaged as being useful in the design of isothermal dies and processes.

Thermal extrusion of starch film with alcohol

A one-step thermal extrusion process has been investigated for the modification of starch with alcohol in order to improve the film properties. Unmodified starch/glycerol mixtures containing Methanol (MetOH), ethanol (EtOH) and their combinations (5, 10 and 15 wt%) were thermally extruded to produce thermoplastic. The final hot-pressed film showed increased stiffness and crystallinity, while having decreased moisture uptake due to oxidation and alcohol complexing molecular interactions. The Young’s Modulus, tensile strength and elongation at break increased by 60%, 15% and 32% respectively, for 5 wt% MetOH derived film, compared to the control. The film moisture content was reduced by up to 15 wt% for 5 wt% EtOH-derived film. Generally the crystallinity increased in the alcohol-derived films due to an increased complexing of alcohol with starch forming the VH polymorph. Fourier transform infra-red (FTIR) and proton nuclear magnetic resonance (1HNMR) spectroscopic analysis were used to discuss the molecular interactions between the starch and alcohol molecules.

Evolution of texture during equal channel angular extrusion of commercially pure aluminum: Experiments and simulations

The evolution of crystallographic texture has been comprehensively studied for commercially pure Al as a function of amount of ECAE deformation for the three major routes of ECAE processing. It has been observed that processing through different routes leads to different type of texture, in both qualitative as well as quantitative sense. The results have been analyzed on the basis of existing concepts on ECAE deformation and simulations have been carried out using the simple shear model of ECAE implemented into the Viscoplastic Self Consistent model of polycrystal plasticity. The simulations revealed that non-octahedral slip is needed to reproduce the experimental texture development.

Evolution of Grain-Boundary Microstructure and Texture in Interstitial-Free Steel Processed by Equal-Channel Angular Extrusion

The equal-channel angular extrusion (ECAE) of Ti-bearing interstitial-free (IF) steel was performed following two different routes, up to four passes, at a temperature of 300 degrees C. The ECAE led to a grain refinement to submicron size. After the second pass, the grain size attained saturation thereafter. The microstructural analysis indicated the presence of coincident-site lattice (CSL) boundaries in significant fraction, in addition to a high volume fraction of high-angle random boundaries and some low-angle boundaries after the deformation. Among the special boundaries, Sigma 3 and Sigma 13 were the most prominent ones and their fraction depended on the processing route followed. A deviation in the misorientation angle distribution from the Mackenzie distribution was noticed. The crystallographic texture after the first pass resembled that of simple shear, with the {112}, {110}, and {123} aligned to the macroscopic shear plane.

Development of novel grain morphology during hot extrusion of magnesium AZ21 alloy

Microstructure and microtexture evolution during static annealing of a hot-extruded AZ21 magnesium alloy was studied. Apart from fine recrystallized equiaxed grains and large elongated deformed grains, a new third kind of abnormal grains that are stacked one after the other in a row parallel to the extrusion direction were observed. The crystallographic misorientation inside these grains was similar to that of the fine recrystallized grains. The large elongated grains exhibited significant in-grain misorientation. A self-consistent mechanistic model was developed to describe the formation of these grain morphologies during dynamic recrystallization (DRX). The texture of pre-extruded material, although lost in DRX, leaves a unique signature which manifests itself in the form of these grain morphologies. The origin of abnormal stacked grains was associated with slow nucleation in pre-extruded grains of a certain orientation. Further annealing resulted in large secondary recrystallized grains with occasional extension twins. (c) 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.