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Effect of heat transfer coefficient h and glass temperature before cooling T0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{0}$$\end{document} on glass transition temperature Tg\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_\mathrm{g}$$\end{document} at mid-plane for different glass thicknesses
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Understanding of heat transfer and development of the temperature field in a glass during tempering is very important because it affects the quality. By numerical modeling, it is possible to study the effect of glass temperature before cooling and the values of heat transfer coefficients which determine the cooling rate and material properties on t...
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Hard-facing process is widely used for improving the wear resistance of mild steel. During the application of hard-facing, due to high temperatures, residual stresses and deformations may occur. The tensile residual stresses may cause crack propagation on the hard-faced part. The purpose of this study is to utilise minimum computer work for minimiz...
Citations
... Likewise, Pourmoghaddam et al. performed a paramet-ric study to analyse the behaviour of residual stresses near holes in glass components (Pourmoghaddam and Schneider 2018). Aronen et al. developed an efficient one-dimensional methodology to analyse the influence of several parameters on the temperature and residual stresses of glass (Aronen and Karvinen 2018). ...
In recent decades, there has been a perceptible transformation in how glass is perceived, evolving from being used for its aesthetic appeal to being acknowledged for its structural capabilities. Structural glass components are most often heat treated to increase their ultimate strength. For this purpose, the tempering process is applied. In this context, air is the quintessential cooling technique employed to rapidly cool and fortify the material due to its associated low cost. Nevertheless, it may encounter certain limitations when quenching low thickness components, making other techniques, such as spray mist cooling, to gain traction. Additionally, glass is a very brittle and sensitive material to local stress concentrations. Thus, depending on how the tempering process is performed, an excessive and/or non-homogeneous cooling might result in local transient stresses, which may exceed the allowable strength and cause premature fracture of the material. To this end, the non-uniform transient stress development during glass tempering is studied based on fluid–structure interaction modelling. In this way, the risk of in-process breakage considering the local phenomena during the glass cooling process is assessed. Water mist cooling is able to temper thin glass but, at the same time, large tensile stresses might develop during the cooling down process. This fact fosters the adoption of an interrupt tempering technique. The obtained numerical results are consistent with previous experimental investigations available in the literature.
... It's important to mention that the average size of the fragments represents the rough measure of the quenching quality or the quality of the temper (Fig. 3). More details about the fragmentation process can be found in the literature [1,2,8,9,14,18,19,22]. ...
This study explores the application of machine learning algorithms for supporting complex product manufacturing quality through a focus on quality assurance and control. We aim to take advantage of ML technics to solve one of the complex manufacturing problems of the tempered glass manufacturing industry as a first attempt to automate product quality prediction and optimization in this industrial field as an alternative to destructive testing methodologies. The choice of this application field was motivated by the lack of a robust engineering technique to assess the production quality in real time; this arises the need of using advanced smart manufacturing solution as AI to save the extremely high cost of destructive tests. As methodology, this paper investigates the performance of machine learning techniques including Ridge Regression, Linear Regression, Light Gradient Boosting Machine, and Lasso Regression, for predicting the product thermal treatment quality within the selected type of industry. In the first part, we applied the selected machine learning models to a dataset collected manually and made up of the more relevant process parameters of the heating and the quenching process. Evaluating the results of the applied models, based on several performance indicators such as mean absolute error, mean squared error, and r-squared, declared that Ridge Regression was the most accurate model with a mean error of 14.33 which is significantly acceptable in a business point of view and not reachable by any human level experience of prediction. The second part consists of developing a digitalized device connected to the manufacturing process to provide predictions in real time. This device operates as an error-proofing system that sends a reverse signal to the machine in case the prediction shows a non-compliant quality of the current processed product. This study can be expanded to predict the optimal process parameters to use when the predicted values do not meet the desired quality and can advantageously replace the trial-and-error approach that is generally adopted for defining those parameters. The contribution of our work relies on the introduction of a clear methodology (from idea to industrialization) for the design and deployment of an industrial-grade predictive solution within a new field which is the glass transformation.
... TA B L E 1 Material properties for the calculation of heat transfer in the annealing lehr TA B L E 3 Characteristics of shear and bulk relaxation times and response function for ultrathin glass (UTG) structural relaxation (T ref = 869 K)[11][12][13][14][15][16] ...
Accurate simulation and measurement of the residual stress are pressing needs in ultrathin glass (UTG) industrial stable production. Herein, the heat transfer in an annealing lehr and the residual stresses at different positions along the width of the UTG ribbon were simulated by the finite element method and measured via the Vickers indentation. The residual stresses at 400 and 600 mm to the edge were large, which caused serious production loss. Besides, we conducted molecular dynamics (MD) simulation to reveal the mechanism for residual stress formation. During UTG cooling, the cooling rate of the core is slower than that of the surface. Due to the influence of the relaxation process, the latter would hinder the former's R–O (where R is Na, Mg, Ca, Al, or Si) length contraction, implying that the surface would generate residual compressive stress. The temperature difference between them increases as the cooling rate grows, leading to the residual stress increase. Finally, based on revealing the formation principle of residual stress by MD, the edge electric heatings were set in zone B, and the residual stresses at 400 and 600 mm to the edge are reduced.
... Cooling down to room temperature was performed with a maximum of 2 K min −1 to remove the residual stresses of both the glass and the densification zone. An explanation of heating influence on glass material properties can be found in Aronen and Karvinen (2018). The absence of residual stresses was verified by a scattered light polariscope. ...
In the present work, subcritical crack growth in soda-lime silicate glass is investigated under different environmental conditions. Crack growth parameters as a function of temperature and humidity were determined by dynamic fatigue tests. The specimens were pre-damaged for constant initial crack lengths in all specimens using the Vickers indenter. The initial flaw size induced by the Vickers indenter was obtained by a scanning electron microscope picture of the fracture surface, which could also show the initial flaw geometry. Furthermore, the influence of humidity and temperature on the failure stress of specimens with a constant initial crack length was simulated and the deviations are shown. A comprehensive version of this investigation is currently (16.03.2021) under review in the Journal for Glass Structures and Engineering.
... The generation of residual stresses during thermal tempering is rather complex, and the theory behind is not indicating that the distribution should be a parabola. In [20], 1D numerical simulations of the tempering process were performed to investigate the effect of temperatures before quenching and cooling rate during the quenching process. The authors assumed equilibrium and a symmetrical stress distribution while performing the numerical simulations. ...
In most literature, the residual stress distribution is assumed to be a symmetrically 2nd order polynomial with compressive stresses near the surface, balanced by tensile stresses in the centre. This assumption leads directly to the assertion that the thickness of the compressive layer is 21.1 % of the total thickness. The present paper experimentally investigates the accuracy of this well-established rule for thermally tempered glass and develops a simple equation for asymmetric stress distributions.
The experimental investigation is based on more than 6000 measurements of commercially tempered (and heat-strengthened) soda lime silica glass and provides statistics for the compressive zone depth. The dependency of the thickness, residual stress state, and the effect of asymmetric stress distributions is investigated.
Due to the scattering in the experimental results, an FE-model has been applied to clarify the effect from the different parameters.
... The calculation formula of ( ) and ( ) is as follows [32]: ...
Curved glass is widely used in 3C industry, and the market demand is increasing gradually. Glass molding process (GMP) is a high-precision, high-efficiency 3D glass touch panel processing technology. In this study, the processing parameters of fingerprint lock glass panels were deeply analyzed. This paper first introduces the molding process of the glass panel, discusses the glass forming device, and explains the heat conduction principle of the glass. Firstly, it introduces the forming process of the glass panel, discusses the glass forming device, and explains the heat conduction principle of the glass. Secondly, the simulation model of a fingerprint lock glass plate was simulated by MSC. Marc software. The stress relaxation model and structure relaxation model are used in the model, and the heat transfer characteristics of glass mold are combined to accurately predict the forming process of glass components. The effects of molding temperature, heating rate, holding time, molding pressure, cooling rate and other process parameters on product quality characteristics (residual stress and shape deviation) were analyzed through simulation experiments. The results show that, in a certain range, the residual stress is inversely proportional to the bending temperature and heating rate, and is directly proportional to the cooling rate, while the shape deviation decreases with the increase of temperature and heating rate. When the cooling rate decreases, the shape deviation first decreases and then increases. Furthermore, a verification experiment is designed to verify the reliability of the simulation results by measuring and calculating the surface roughness of the formed products.
... The time delay causes a transient stress profile which starts with a tense surface, whereby the tensile zone is (due to the gradient in fictive temperature) gradually shifting towards the center of the material, while a compressive layer is build-up at the surface. 9 This compressive layer evolves into the persistent surface compressive zone once the glass product is fully cooled to below ~0.8 T g and the thermal gradient has vanished. Typical surface compressive stresses which are achieved in this way are in the range of 100 MPa, usually in glasses with a wall thickness of about 3 mm or above. ...
Thermal strengthening remains the primary method for enhancing the practical strength of commodity glass products, however, the process is limited in terms of applicable glass thickness and coefficient of thermal expansion. The primary reasons for this limitation are the achievable heat transfer coefficient when using conventional gas cooling, and the occurrence of transient surface tension in the early stages of rapid quenching. We revisit this problem for the case of thin borosilicate glass sheet. Using liquid gallium as the cooling medium, ultra‐fast heat extraction is achieved, with a heat transfer coefficient exceeding 5000 Wm⁻² K⁻¹. The low vapor pressure of gallium even at high temperatures enables preheating to a wide range of sheet entrant temperatures. We demonstrate thermal strengthening of low‐expansion borosilicate glass with persistent surface compression of up to 85 MPa, and quenching to a fictive temperature of ~190 K above the glass transition temperature. Glass sheet obtained in this way exhibits notably enhanced surface defect resistance to sharp indentation. In addition to thermal strengthening, the extraordinarily high heat extraction rates achieved by liquid metal immersion enable exploitation of high‐Tf glass properties beyond small and thin sample geometry.
... Cooling down to room temperature was performed with a maximum of 2 K min −1 to remove the residual stresses of both the glass and the densification zone. An explanation of heating influence on glass material properties can be found in Aronen and Karvinen (2018). The absence of residual stresses was verified by a scattered light polariscope. ...
In the present work, subcritical crack growth in soda-lime silicate glass is investigated under different environmental conditions. Crack growth parameters as a function of temperature and humidity were determined by dynamic fatigue tests, which has been verified by using the in-situ method of filming crack growth during experiments. The specimens were pre-damaged for constant initial crack lengths in all specimens using the Vickers indentation test. The determined parameters were compared with those from literature in order to discuss existing deviations of sub-critical crack growth parameters in literature. These deviations may be caused by environmental conditions and different chemical compositions of the glass. Arrest lines were used to determine the ratio of crack width to crack depth in Vickers indented specimens. For the initial crack depth, images of fracture surfaces were taken using an scanning electron microscope. Furthermore , the influence of humidity and temperature on the failure stress of unindented specimens with a constant initial crack length was simulated.
... It was found that there is a response relationship between residual stress and process parameters. Aronen [21,22] studied the effect of glass plate temperature, thermal conductivity and brace layout on glass deformation by establishing simulation model. It was found that increasing temperature could improve the thermal conductivity of the system and could change the mechanical properties of the glass. ...
Glass multi-station bending machining (GMBM) is a high-precision and efficient glass processing technique for smartphone curved screen in 3C industry. In this paper, simulation model of the GMBM of smartphone curved screen was researched by using MSC Marc software. The stress relaxation and structural relaxation models of glass material were used in the numerical model to accurately predict the forming process of the glass component. The effects of process parameters of GMBM, namely heating rate (HR), holding time, bending temperature (BT), bending pressure and cooling rate (CR), on the product quality characteristics (residual stress and shape deviation) and energy efficiency were analyzed based on orthogonal experiments. It can be found that the BT, CR and HR have extremely important effects on product residual stress, shape deviation and energy efficiency. Furthermore, a multi-objective optimization method based on NSGA-III (a non-dominant sorting genetic algorithms based on reference points) was applied to efficiently solve the optimization problem between glass product quality and energy efficiency. The optimal parameter schemes with high quality and low energy efficiency were obtained by the Pareto front of multi-objective, and the average prediction errors of the numerical results by the optimized schemes are no more than 20% through confirm experiments. The optimized schemes improve the stability of the process of GMBM, which can deal with the challenge of green manufacturing.
... By imposing a compressive residual stress at the surface, the surface flaws will be in a permanent state of compression which has to be exceeded by externally imposed stress before failure can occur (Schneider 2001;Nielsen et al. 2010;Pourmoghaddam et al. 2016;Pourmoghaddam and Schneider 2018a). The amount of the residual surface compressive stress largely depends on the cooling rate and therefore on the heat transfer coefficient between the glass and the cooling medium (Gardon 1965;Aronen and Karvinen 2017). However, thermally tempered glass will fragmentize completely into many pieces, if the equilibrated residual stress state within the glass plate is disturbed sufficiently and if the elastic strain energy in the glass is large enough, Fig. 1. ...
This work deals with the prediction of glass breakage. A theoretical method based on linear elastic fracture mechanics (LEFM) merged with approaches from stochastic geometry is used to predict the 2D-macro-scale fragmentation of glass. In order to predict the fragmentation of glass the 2D Voronoi tesselation of distributed points based on spatial point processes is used. However, for the distribution of the points influence parameters of the fracture structure are determined. The approach is based on two influencing parameters of fragment size and fracture intensity , which are described in this paper. The Fragment Size Parameter describes the minimum distance between the points and thus the size of a fragment. It is derived from the range of influence of the remaining elastic strain energy in a single fragment taking into account the LEFM based on the energy criterion of Griffith. It considers the extent of the initial elastic strain energy before fragmentation obtained from the residual stress as well as a ratio of the released energy due to fragmentation. The Fracture Intensity Parameter describes the intensity of the fragment distribution, and thus the empirical reality of a fracture pattern. It can be obtained by statistical evaluation of the fracture pattern. In this work, the fracture intensity is determined from the experimental data of fracture tests. The intensity of a fracture is the quotient of the number of fragments in an observation field and its area and is assumed to be constant in the observation filed. The fracture intensity and the correlation between a constant intensity and the Fragment Size Parameter was determined. The presented methodology can also generally be used for the prediction of fracture patterns in brittle materials using a Voronoi tesselation over random fields.