Numerical solution of the pressing devices shape optimization problem in the glass industry

In this contribution, we present the problem of shape optimization of the plunger cooling which comes from the forming process in the glass industry. We look for a shape of the inner surface of the insulation barrier located in the plunger cavity so as to achieve a constant predetermined temperature on the outward surface of the plunger. A rotationally symmetric system, composed of the mould, the glass piece, the plunger, the insulation barrier and the plunger cavity, is considered. The state problem is given as a multiphysics problem where solidifying molten glass is cooled from the inside by water flowing through the plunger cavity and from the outside by the environment surrounding the mould.The cost functional is defined as the squared \(L^2_r\) norm of the difference between a prescribed constant and the temperature on the outward boundary of the plunger. The temperature distribution is controlled by changing the insulation barrier wall thickness.The numerical results of the optimization to the required target temperature 800 ?C of the outward plunger surface together with the distribution of temperatures along the interface between the plunger and the glass piece before, during and after the optimization process are presented.     

Water absorption and swelling of glass/epoxy syntactic foams

The results of experimental and theoretical investigation of glass/epoxy syntactic foams at a long-term (10 years) exposure in water are presented. Specimens for experimental investigation were made from EDT-10 epoxy filled with MSO-779 hollow glass spheres. Seven types of specimens with filler volume fraction varying from 0 to 0.6 were tested. The curves of long-term water absorption and swelling were determined. It was expected that the addition of hollow glass spheres must substantially reduce the sorptional capacity of material because of the reduction of the volume content of the matrix and, therefore, because of reduction of the part of the volume where the molecules of water can diffuse. However, the water absorption process in syntactic foams was found to continue during the total term of the experiments without a tendency to stop. After ten years the limiting equilibrium state was not achieved and the concentration of water in composite specimens became higher than the equilibrium concentration of water in unfilled EDT-10 epoxy. In long-term tests the swelling strain was found to be a nonlinear function of water content. The degree of nonlinearity increased when the volume content of the filler was increased. The calculational prediction of absorption and swelling curves of syntactic foams with different volume contents of the filler was done using the experimentally determined characteristics of absorption of the matrix. The water transport process in the matrix was considered to obey Fick's law. It was found that the initial parts of the experimental curves (during the first year of exposure) show a good enough agreement with calculated data for engineering applications. Subsequently, the discrepancy between the experimental results and calculated data increased and reached such large values that the predicted results became unacceptable. The possible reasons of such discrepancy (breaking of adhesion bonds between the matrix and the filler with subsequent sorption of water at the glass sphere surface, and diffusional filling by water of the inner parts of the damaged glass spheres, etc.) are discussed.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October, 1995. University of Colima, Colima City, Colima, Mexico. Institute of Polymer Mechanics, Latvian Academy of Sciences, Riga, LV-1006, Latvia. Published in Mekhanika Kompozitnykh Materialov, No. 1, pp. 83–97, January–February, 1996.     

Electromagnetic flow rate measurement in turbulent liquid metal channel flow

Flow control in hot aggressive melts is a big challenge for metallurgical and glass technology applications. For instance, during the production of float glass, the glass melt solidifies on the top of a liquid tin bath. To achieve a spatially homogeneous glass thickness, both global and local control of the thermofluiddynamic transport phenomena in the tin bath are crucial. The concept a global flow control involves the coupling of the non-contact electromagnetic flow rate measurement technique of Lorentz force velocimetry and the non-contact flow driving technique of electromagnetic pumps based on rotating permanent magnets. The paper presents a model experiment using the low-melting test melt GaInSn as well as numerical simulations using the commercial code FLUENT/MHD. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Delamination of Grain-Interfaces in Silicon Nitride

Intergranular cracking due to delamination of grain interfaces along with the development of bridging grains is the most important mechanism for the high fracture toughness of silicon nitride. In this line, an interface behavior, which is extending the Coulomb friction concept into the tensile domain has been implemented into a thermodynamical consistent frame work of Helmholtz free energy and dissipation. The model is used to describe the fracture process in a simple model geometry with a β-Si₃N₄ grain embedded into a precracked matrix of oxynitride glass. The material model considers the thermoelastic anisotropy of the grain and the thermal residual stresses, which evolve during the cooling of the model from the glass transition temperature to room temperature. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Determination of the residual stresses in the welded joints of glass structures

We propose a computational model for determining the residual stresses in a welded glass structure taking account of the properties of the formation of residual stresses in glass. The problem is solved in displacements using Galerkin's method in conjunction with a finite-element model. A numerical solution is obtained for the axisymmetric case. Translated fromMatematichni Metodi ta Fiziko-mekhanichni Polya, Vol. 39, No. 1, 1996, pp. 131–134.     

Isotropic model of quadrupole glass. II. Breaking of replica symmetry

In a model of an isotropic quadrupole glass with two order parameters, a macroscopically large number of metastable states is found at zero temperature. The replica symmetry is broken in the immediate vicinity of the transition to the glass state, and it is shown that the obtained solution is stable.L. F. Vershchagin Institute of High Pressure Physics, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 91, No. 1, pp. 157–167, April, 1992.     

Maximum force of friction in rubber-metal friction pairs under conditions of constant compressive deformation of the rubber

The maximum force of friction at the initial moment of slip has been investigated on rubber-metal friction pairs under conditions of constant compressive deformation of the rubber during transition from the high-elastic to the glassy state. Filled butadiene-nitrile rubber compounds were studied in the temperature range from +20 to –50°C. The temperature dependence of the maximum force of friction has a sharply expressed maximum near the glass transition temperature. As the temperature falls, the force of friction at first increases, in accordance with the molecular-kinetic theory. As the temperature continues to fall, in the transition region the maximum force of friction begins to rise more sharply owing to a sharp increase in the volume-mechanical friction component. The fall in the maximum force of friction below the glass transition point associated with a decrease in the deformed volume of rubber due to shrinkage and with the reduced mechanical loss factor.Mekhanika Polimerov, Vol. 3, No. 3, pp. 533–538, 1967     

Experimental study of the effect of technological parameters on the residual stresses in thin-walled coiled parts

The effect of the parameters of heat treatment and programmed winding under tension on the residual stresses in thin-walled coiled parts made from glass plastic by the "dry" winding of a heated glass strip on an unheated mandrel is studied experimentally. The effect of the thickness of the parts on the maximum radial residual stresses is considered. A method is proposed for regulating the residual stresses in parts with very thick walls.Translated from Mekhanika Polimerov, No. 1, pp. 75–80, January–February, 1972.     

Optimal boundary control of glass cooling processes

In this paper, an optimal control problem for glass cooling processes is studied. We model glass cooling using the SP1 approximations to the radiative heat transfer equations. The control variable is the temperature at the boundary of the domain. This results in a boundary control problem for a parabolic/elliptic system which is treated by a constrained optimization approach. We consider several cost functionals of tracking‐type and formally derive the first‐order optimality system. Several numerical methods based on the adjoint variables are investigated. We present results of numerical simulations illustrating the feasibility and performance of the different approaches. Copyright © 2004 John Wiley & Sons, Ltd.     

Elastoplastic deformations of metal pressure vessels reinforced with unidirectional glass-reinforced plastic

The design of cylindrical shells reinforced in the circumferential direction with high-strength elastic fibers is considered. The problem is solved on the basis of the deformation and flow theories. Relations are derived for the layer thickness required to obtain a structure of uniform strength and for the tension that must be applied to the glass tape during winding.Moscow Ordzhonikidze Aviation Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1069–1074, November–December, 1969.     

多层玻璃窗隔声效果的数学模型分析

借助物理学声波传播理论,研究单层玻璃隔声的衡量方法,推导出双层窗户比单层窗户隔声效果好的数学模型为I4″/I2=(1-α1)(l-α2)/e2α11,并探讨在有限的建筑材料规定下实现隔声效果最佳的方法.     

Relationship between strength characteristics of unidirectional glass-reinforced plastics and their composition

The article discusses the effect of the amount of binder present and the porosity of the glass reinforced plastic on the usable strength of the glass fibers, the tensile strength, and the elasticity module in stretching. It is shown that a relationship exists over the whole range tested between the volume ratio of the components (binder and glass fiber), certain strength characteristics, and porosity. A method is suggested for the comparison of glass-reinforced plastics according to their usable fiber strength which can be used for the selection of the best binder, the glass material, the glass composition, glass fibers, the lubricant, the technological scheme, etc.Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 477–480, May–June, 1970.     

Modification of glass-filled polyamide 66 by reactive oligoorganosilane

Properties of glass-filled polyamide 66 modified by reactive oligoorganosilane were investigated. It was found that modification led to the improvement of the rheological properties of polyamide. The addition of the modifier decreased the glass transition temperature T_g of the polyamide from 60 to 50–59°C, without affecting the melting point. Composites modified by oligoorganosilane are characterized by higher (10–40°C) temperatures of onset and 50% weight loss as compared to the initial composite. It was found that chemical reaction of oligoorganosilane with polyamide and glass fibers took place during coextrusion of the modifier and polyamide, which formed firm chemical bonds between the polyamide and filler and thus favored a considerable improvement in the physicomechanical properties of the composite. The change in the structure and properties of the polyamide observed during modification by oligoorganosilane significantly affected its behavior during friction. The modification made it possible to increase the wear resistance of the composite 1.5 to 2 times and to decrease its friction coefficient from 0.38 to 0.27–0.33. It was also found that the ability of oligoorganosilane to react during its processing with water in the polyamide allowed for a significant decrease in the intensity of hydrolytic processes in the polymer. Because of this, the physicomechanical, rheological, and antifrictional properties of modified composites with an increased content of moisture (up to 3%) in the initial polyamide surpass similar characteristics of the composites containing no modifier, with not only enhanced but also optimum (0.2%) humidity of polymer granules.Nesmeyanov Institute of Organoelement Compounds, Russian Academy of Sciences, Moscow, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 4, pp. 545–553, July–August, 1998.     

Determination of the reliability of glass structures with steady and alternating loads

A method is developed for determining the reliability (nonfailure probability) of glass structures for a prescribed loading duration by alternating loads; an equation is obtained for calculating the reliability of glass structures from material (glass) strength parameters. It is shown that reliability with steady loads is a particular case of reliability with alternating loads. The method developed is based on a correlation established between long-term strength of the material and glass structure, and use of a new criterion of equal reliabilities for alternating loads.Lvov. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 21, pp. 90–97, 1990.     

Effect of surface modification on the adhesion and mechanical properties of glass-reinforced plastics

The adhesion of an epoxy-polyester resin to glass fibers with clean and modified surfaces has been determined. The effect of this adhesion on some of the properties of glass-reinforced plastics (bending, tension, shear) is investigated.Mekhanika polimerov, Vol. 1, No. 1, pp. 93–99, 1965     

Multifibre polymer composites: Prediction of deformation and thermophysical properties

Conclusions A theoretical and experimental investigation was carried out to examine the possibilities of a structural approach for prediction of elastic constants, creep functions and thermophysical characteristics of hybrid polymer composites reinforced with anisotropic fibres of several types. The theoretical solutions were obtained by generalizing the self-consistent method for the case of a three phase model. The effects of brittle fibre breakdown under tension in the direction of reinforcement of a unidirectional hybrid composite were studied under conditions of a short-term loading and a long-term creep. It has been shown that a creep of viscoelastic fibres plays a principal role in creep of the hybrid composite. It is just this creep that significantly increases the fibre damage during creep of the composite.A variant of the solution has been proposed for predicting the thermorheologically complex behavior of hybrid composites containing not only elastic but also viscoelastic thermorheologically simple components with different temperature-time shift factors. The peculiarities of thermal expansion of hybrid composites and the possibilities for a purposeful control of thermal expansion coefficients by hybridization were studied. The considered thermal interval included a region of transition of the polymer matrix from a glass state into a viscoelastic one.The control tests were performed for specimens of organic/glass, organic/carbon, glass/carbon and organic/boron polymer composites with different ratios of fibre volume contents. On the whole, the obtained accuracy of predicting the characteristics of the examined hybrid composites may be considered as acceptable for engineering applications.Published in Mekhanika Kompozitnykh Materialov, Vol. 30, No. 3, pp. 299–313, May–June, 1994.     

Friction and rheological properties of resin-impregnated glass tape

The dependence of the dynamic coefficient of friction of resin-impregnated glass tape on the sliding speed over the mandrel surface and the viscosity of the resin is derived. The formulas obtained are confirmed by the results of experiments which indicate a linear dependence of the coefficient of friction on the sliding speed of the tape over a metal mandrel. Graphically, this dependence is expressed by straight lines with a common origin and a slope that increases with the viscosity of the resin. The coefficient of friction of glass tape sliding over a prewound layer at low speeds also has a linear dependence. At high speeds the dependence takes the form of a damped curve.Translated from Mekhanika Polimoerov, No. 1, pp. 166–170, January–February, 1976.     

Characteristics of stretching of high-impact polystyrene and polycarbonate close to the glass transition temperature

A study has been made of the stress-strain characteristics of high-impact composites based on poly sty renes (PS) or polycarbonates (PC) in uniaxial stretching at temperatures close to the glass transition temperature of the matrix material Heterogeneity of the structure of the material at the microlevel, owing to the presence of a graft copolymer in the PS composites or the presence of polyethylene terephthalate (a reactive additive) in the PC, tends to lower the effective glass transition temperature as determined at high elongations. Weak interaction of the impact-strength modifiers with the matrix material (determining the heterogeneity of the structure at the macrolevel) results in a lower stability of uniform stretching in the region of the high-elastic state, but increases the values of the elongation at break in the transition region from the glassy state to the high-elastic state. From the standpoint of achieving high strength and deformability of high-impact composites during their processing, the structure should be organized so as to provide optimal heterogeneity at both the microlevel and macrolevel.Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 4, pp. 509–517, July–August, 1995.     

On a 1-D Model of Stress Relaxation in an Annealed Glass

A 1-D model of a slab of glass of a small thickness is considered. The governing equations are those of the classical 1-D linear viscoelasticity. A load due to the temperature gradients is assumed. The aim is to model the process called annealing. It is shown that an additional load due to structural strain is crucial for the success of the model. Algorithms of a numerical solution of the governing equations are proposed. Numerical results are presented and commented.     

Singularity of the “swallow-tail” type and the glass-glass transition in a system of collapsing hard spheres

In the mode-coupling approximation, we consider the transition to the glass state in a system of collapsing hard spheres (a system with the hard-core potential to which a repulsive step is added). We propose an approximation for the structure factor of the system, which we use to construct the phase diagram of the transition to the glass state. We show that there exists a maximum on the liquid-glass curve corresponding to the reentrant transition to the glass state in the system. In the framework of the proposed model, we consider bifurcations of solutions of the equations describing the transition to the glass state and show that there exist bifurcations of the “swallow-tail” type corresponding to the glass-glass transition.