The mechanics of the conform continuous extrusion process

The work describes the programme of activities relating to a mechanical study of the Conform extrusion process. The main objective was to provide a basic understanding of the mechanics of the Conform process with particular emphasis placed on modelling using experimental and theoretical considerations. The experimental equipment used includes a state of the art computer-aided data-logging system and high temperature loadcells (up to 260oC) manufactured from tungsten carbide. Full details of the experimental equipment is presented in sections 3 and 4. A theoretical model is given in Section 5. The model presented is based on the upper bound theorem using a variation of the existing extrusion theories combined with temperature changes in the feed metal across the deformation zone. In addition, constitutive equations used in the model have been generated from existing experimental data. Theoretical and experimental data are presented in tabular form in Section 6. The discussion of results includes a comprehensive graphical presentation of the experimental and theoretical data. The main findings are: (i) the establishment of stress/strain relationships and an energy balance in order to study the factors affecting redundant work, and hence a model suitable for design purposes; (ii) optimisation of the process, by determination of the extrusion pressure for the range of reduction and changes in the extrusion chamber geometry at lower wheel speeds; and (iii) an understanding of the control of the peak temperature reach during extrusion.

Mechanical properties of sheet metal under forming conditions

In the bulge test, a sheet metal specimen is clamped over a circular hole in a die and formed into a bulge by the hydraulic pressure on one side of the specirnen. As the unsupported part of the specimen is deformed in this way, its area is increased, in other words, the material is generally stretched and its thickness generally decreased. The stresses causing this stretching action are the membrane stresses in the shell generated by the hydraulic pressure, in the same way as the rubber in a toy balloon is stretched by the membrane stresses caused by the air inside it. The bulge test is a widely used sheet metal test, to determine the "formability" of sheet materials. Research on this forming process (2)-(15)* has hitherto been almost exclusively confined to predicting the behaviour of the bulged specimen through the constitutive equations (stresses and strains in relation to displacements and shapes) and empirical work hardening characteristics of the material as determined in the tension test. In the present study the approach is reversed; the stresses and strains in the specimen are measured and determined from the geometry of the deformed shell. Thus, the bulge test can be used for determining the stress-strain relationship in the material under actual conditions in sheet metal forming processes. When sheet materials are formed by fluid pressure, the work-piece assumes an approximately spherical shape, The exact nature and magnitude of the deviation from the perfect sphere can be defined and measured by an index called prolateness. The distribution of prolateness throughout the workpiece at any particular stage of the forming process is of fundamental significance, because it determines the variation of the stress ratio on which the mode of deformation depends. It is found. that, before the process becomes unstable in sheet metal, the workpiece is exactly spherical only at the pole and at an annular ring. Between the pole and this annular ring the workpiece is more pointed than a sphere, and outside this ring, it is flatter than a sphere. In the forming of sheet materials, the stresses and hence the incremental strains, are closely related to the curvatures of the workpiece. This relationship between geometry and state of stress can be formulated quantitatively through prolateness. The determination of the magnitudes of prolateness, however, requires special techniques. The success of the experimental work is due to the technique of measuring the profile inclination of the meridional section very accurately. A travelling microscope, workshop protractor and surface plate are used for measurements of circumferential and meridional tangential strains. The curvatures can be calculated from geometry. If, however, the shape of the workpiece is expressed in terms of the current radial (r) and axial ( L) coordinates, it is very difficult to calculate the curvatures within an adequate degree of accuracy, owing to the double differentiation involved. In this project, a first differentiation is, in effect, by-passed by measuring the profile inclination directly and the second differentiation is performed in a round-about way, as explained in later chapters. The variations of the stresses in the workpiece thus observed have not, to the knowledge of the author, been reported experimentally. The static strength of shells to withstand fluid pressure and their buckling strength under concentrated loads, both depend on the distribution of the thickness. Thickness distribution can be controlled to a limited extent by changing the work hardening characteristics of the work material and by imposing constraints. A technique is provided in this thesis for determining accurately the stress distribution, on which the strains associated with thinning depend. Whether a problem of controlled thickness distribution is tackled by theory, or by experiments, or by both combined, the analysis in this thesis supplies the theoretical framework and some useful experimental techniques for the research applied to particular problems. The improvement of formability by allowing draw-in can also be analysed with the same theoretical and experimental techniques. Results on stress-strain relationships are usually represented by single stress-strain curves plotted either between one stress and one strain (as in the tension or compression tests) or between the effective stress and effective strain, as in tests on tubular specimens under combined tension, torsion and internal pressure. In this study, the triaxial stresses and strains are plotted simultaneously in triangular coordinates. Thus, both stress and strain are represented by vectors and the relationship between them by the relationship between two vector functions. From the results so obtained, conclusions are drawn on both the behaviour and the properties of the material in the bulge test. The stress ratios are generally equal to the strain-rate ratios (stress vectors collinear with incremental strain vectors) and the work-hardening characteristics, which apply only to the particular strain paths are deduced. Plastic instability of the material is generally considered to have been reached when the oil pressure has attained its maximum value so that further deformation occurs under a constant or lower pressure. It is found that the instability regime of deformation has already occurred long before the maximum pressure is attained. Thus, a new concept of instability is proposed, and for this criterion, instability can occur for any type of pressure growth curves.

Vitamin C supplementation in normal subjects reduces constitutive ICAM-1 expression

Regulation of monocyte adhesion molecule gene expression is via redox sensitive transcription factors. We have investigated whether dietary antioxidant supplementation with vitamin C (250mg/day) can modulate monocyte ICAM-1 expression in healthy male subjects with low plasma vitamin C at baseline. In a randomised, double-blind, crossover study, monocyte ICAM-1 mRNA was analysed using quantitative reverse transcriptase PCR. Protein was determined by flow cytometry (monocytes) and ELISA (plasma). Monocyte numbers were unaltered by supplementation. Subjects with low plasma vitamin C (<50μM) prior to supplementation expressed higher levels of monocyte ICAM-1mRNA, and showed a significant (50%) reduction in ICAM-1mRNA expression after 6 weeks of 250mg/day vitamin C supplementation (p<0.05). This was paralleled by a reduction in sICAM-1 (p<0.05). For the first time, these results show that dietary vitamin C can modulate monocyte ICAM-1 gene expression in vivo, where regulation of gene expression represents a novel mechanism for benefit from dietary antioxidants. © 2003 Elsevier Inc. All rights reserved.

Dietary supplementation with vitamin C but not vitamin E reduces constitutive expression of ICAM-1 in peripheral blood monocytes of normal subjects with low plasma vitamin C levels

Monocytes play a central role in inflammatory responses through systemic antigen presentation and cytokine secretion. Regulation of monocyte adhesion molecule and inflammatory gene expression is via redox sensitive transcription factors. Therefore we have investigated the hypothesis that dietary antioxidant supplementation with vitamins C (250mg/d) or E (400iU/d) for six weeks can modulate monocyte ICAM-1 expression in healthy male subjects with low plasma vitamin C at baseline. In a randomised, double-blind, crossover study, ICAM-1 mRNA and protein was analysed using quantitative RTPCR with ELISA measurement of PCR products and by flow cytometry and ELISA respectively. Monocyte numbers were unaltered by supplementation. Subjects with low plasma vitamin C (<50uM) prior to supplementation expressed higher levels of monocyte ICAM-1 mRNA, and showed a significant (50%) reduction in ICAM-1 mRNA expression after 6 weeks of 250mg/d vitamin C supplementation compared to subjects with normal plasma vitamin C. This was paralleled by a reduction in plasma sICAM-1. Vitamin E supplementation had no effect on ICAM-1 expression. For the first time, these results show that dietary vitamin C can modulate monocyte ICAM-1 gene expression in vivo, where regulation of gene expression represents a novel mechanism for benefit from dietary antioxidants.

Gaussian process approximations of stochastic differential equations

Stochastic differential equations arise naturally in a range of contexts, from financial to environmental modeling. Current solution methods are limited in their representation of the posterior process in the presence of data. In this work, we present a novel Gaussian process approximation to the posterior measure over paths for a general class of stochastic differential equations in the presence of observations. The method is applied to two simple problems: the Ornstein-Uhlenbeck process, of which the exact solution is known and can be compared to, and the double-well system, for which standard approaches such as the ensemble Kalman smoother fail to provide a satisfactory result. Experiments show that our variational approximation is viable and that the results are very promising as the variational approximate solution outperforms standard Gaussian process regression for non-Gaussian Markov processes.

The variant rpoS allele of S. enteritidis strain 27655R does not affect virulence in a chick model nor constitutive curliation but does generate a cold-sensitive phenotype

Adherence of pathogenic Escherichia coli and Salmonella spp. to host cells is in part mediated by curli fimbriae which, along with other virulence determinants, are positively regulated by RpoS. Interested in the role and regulation of curli (SEF17) fimbriae of Salmonella enteritidis in poultry infection, we tested the virulence of naturally occurring S. enteritidis PT4 strains 27655R and 27655S which displayed constitutive and null expression of curli (SEF17) fimbriae, respectively, in a chick invasion assay and analysed their rpoS alleles. Both strains were shown to be equally invasive and as invasive as a wild-type phage type 4 strain and an isogenic derivative defective for the elaboration of curli. We showed that the rpoS allele of 27655S was intact even though this strain was non-curliated and we confirmed that a S. enteritidis rpoS::strr null mutant was unable to express curli, as anticipated. Strain 27655R, constitutively curliated, possessed a frameshift mutation at position 697 of the rpoS coding sequence which resulted in a truncated product and remained curliated even when transduced to rpoS::strr. Additionally, rpoS mutants are known to be cold-sensitive, a phenotype confirmed for strain 27655R. Collectively, these data indicated that curliation was not a significant factor for pathogenesis of S. enteritidis in this model and that curliation of strains 27655R and 27655S was independent of RpoS. Significantly, strain 27655R possessed a defective rpoS allele and remained virulent. Here was evidence that supported the concept that different naturally occurring rpoS alleles may generate varying virulence phenotypic traits.

Constitutive glycogen synthase kinase-3α/β activity protects against chronic β-adrenergic remodelling of the heart

Aims - Glycogen synthase kinase 3 (GSK-3) signalling is implicated in the growth of the heart during development and in response to stress. However, its precise role remains unclear. We set out to characterize developmental growth and response to chronic isoproterenol (ISO) stress in knockin (KI) mice lacking the critical N-terminal serines, 21 of GSK-3 and 9 of GSK-3 respectively, required for inactivation by upstream kinases. Methods and results - Between 5 and 15 weeks, KI mice grew more rapidly, but normalized heart weight and contractile performance were similar to wild-type (WT) mice. Isolated hearts of both genotypes responded comparably to acute ISO infusion with increases in heart rate and contractility. In WT mice, chronic subcutaneous ISO infusion over 14 days resulted in cardiac hypertrophy, interstitial fibrosis, and impaired contractility, accompanied by foetal gene reactivation. These effects were all significantly attenuated in KI mice. Indeed, ISO-treated KI hearts demonstrated reversible physiological remodelling traits with increased stroke volume and a preserved contractile response to acute adrenergic stimulation. Furthermore, simultaneous pharmacological inhibition of GSK-3 in KI mice treated with chronic subcutaneous ISO recapitulated the adverse remodelling phenotype seen in WT hearts. Conclusion - Expression of inactivation-resistant GSK-3/does not affect eutrophic myocardial growth but protects against pathological hypertrophy induced by chronic adrenergic stimulation, maintaining cardiac function and attenuating interstitial fibrosis. Accordingly, strategies to prevent phosphorylation of Ser-21/9, and consequent inactivation of GSK-3/, may enable a sustained cardiac response to chronic-agonist stimulation while preventing pathological remodelling. © 2010 The Author.

Fast reconstruction of harmonic functions from Cauchy data using the Dirichlet-to-Neumann map and integral equations

We propose and investigate a method for the stable determination of a harmonic function from knowledge of its value and its normal derivative on a part of the boundary of the (bounded) solution domain (Cauchy problem). We reformulate the Cauchy problem as an operator equation on the boundary using the Dirichlet-to-Neumann map. To discretize the obtained operator, we modify and employ a method denoted as Classic II given in [J. Helsing, Faster convergence and higher accuracy for the Dirichlet–Neumann map, J. Comput. Phys. 228 (2009), pp. 2578–2576, Section 3], which is based on Fredholm integral equations and Nyström discretization schemes. Then, for stability reasons, to solve the discretized integral equation we use the method of smoothing projection introduced in [J. Helsing and B.T. Johansson, Fast reconstruction of harmonic functions from Cauchy data using integral equation techniques, Inverse Probl. Sci. Eng. 18 (2010), pp. 381–399, Section 7], which makes it possible to solve the discretized operator equation in a stable way with minor computational cost and high accuracy. With this approach, for sufficiently smooth Cauchy data, the normal derivative can also be accurately computed on the part of the boundary where no data is initially given.

A variational method and approximations of a Cauchy problem for elliptic equations

A Cauchy problem for general elliptic second-order linear partial differential equations in which the Dirichlet data in H½(?1 ? ?3) is assumed available on a larger part of the boundary ? of the bounded domain O than the boundary portion ?1 on which the Neumann data is prescribed, is investigated using a conjugate gradient method. We obtain an approximation to the solution of the Cauchy problem by minimizing a certain discrete functional and interpolating using the finite diference or boundary element method. The minimization involves solving equations obtained by discretising mixed boundary value problems for the same operator and its adjoint. It is proved that the solution of the discretised optimization problem converges to the continuous one, as the mesh size tends to zero. Numerical results are presented and discussed.

Boundary integral equations for acoustical inverse sound-soft scattering

The shape of a plane acoustical sound-soft obstacle is detected from knowledge of the far field pattern for one time-harmonic incident field. Two methods based on solving a system of integral equations for the incoming wave and the far field pattern are investigated. Properties of the integral operators required in order to apply regularization, i.e. injectivity and denseness of the range, are proved.

Some aspects of the solution of non-linear differential equations

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