Calculation of Residual Stresses in Glass

The viscoelastic nature of bulk metallic glasses (BMGs), their low thermal conductivity, and the fast cooling used in their processing subject them to thermal tempering. This process leads to a residual stress state in which compression on the surface is balanced by tension in the interior. For the first time, we have calculated such stresses in metallic glasses by adapting an analytical instant-freezing model previously developed for silicate glasses. This model has been demonstrated to be reasonably accurate in predicting the final residual stresses, although, due to its very nature, it neglects transient effects. For an infinite plate geometry and employing processing parameters often used for metallic glasses, we predict that significant residual stresses can be generated in these materials during thermal tempering. Preliminary measurements conducted using the layer-removal method yield compressive residual stress values close to model predictions.

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“…[14] and [15], the function ⑀ res (x) Ϫ ⑀ res (x) can be evaluated, avoiding double integration of Eq. [14].…”

Section: Indenbom's Instant-freezing Theory For Infinite Plate Gementioning

confidence: 99%

“…They were then followed by the relaxed by viscous flow. Thus, stresses developed before the viscoelastic [12,13,14] and structural theories. [15] (Refer to the entire cross section solidifies are lower than those in an article by Gardon [4] for the historical development and a detailed comparison of these theories.)…”

Section: Introductionmentioning

confidence: 99%

Thermal-tempering analysis of bulk metallic glass plates using an instant-freezing model

Aydıner

Ü:Ustü:UndaG

Hanan

2001

Metall Mater Trans A

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“…Narayanaswamy and Gardon [6] showed that these differences result from the numerical solution procedure used. In particular, the trapezoidal rule used by Lee et al to approximate the integrals results in large errors when the kernel is strongly nonlinear, which is the case when a glass slab is cooled from a state well above the glass critical temperature.…”

Section: Research Reviewmentioning

confidence: 98%

Modeling and simulation of residual stresses during glass bulb pressing process

Zhou

2007

SCI CHINA SER E

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The residual stresses accumulated in the forming process have great effects on the product quality of the glass bulb. Based on the characteristics analysis of glass bulb forming, a mathematical model has been established for calculating residual stresses of glass pressing process. The material is assumed as thermorheologically simple thermoviscoelastic material, and the flow-induced stress is neglected. The consequences of equilibrium and compatibility equations are discussed in detail, and the boundary conditions are specified for various stages of the forming process. The numerical solution is based on the theory of thin layers, combined with finite difference method in the time and layer difference in the thickness direction. The presented model and solution method could easily be extended to general pressing process of glass, and applied to problems relative to glass pressing, providing extensive reference values.glass bulb, residual stresses, mathematical modeling, numerical simulation, theory of thin layers With the rapid development of electronic products such as TV sets and computers, the need for glass bulb as upper products of color picture tubes also increases greatly. A glass bulb consists of a panel and a cone, which are both pressed in a special press table.In forming, molten glass is pressed into a relatively cold mold, in which complicated and transient flow occurs. Glass melt with high temperature in the core flows toward the mold wall in the glass/air interface of front ceaselessly, which is called as fountain flow. After pressing, the melt is pressurized by pressure of the plunge until the plunger is removed. Because of the mold and air cooling, the layers that come into contact with the mold surface in pressing solidify immediately. And the part will solidify from surface toward core after pressing. The specific volume of glass varies with the changes of temperature. The solidification and shrinkage layer by layer of glass result in a buildup of self-equilibrating residual stresses. Because glass exhibits time-dependent (viscoelastic) thermomechanical behavior, the local stresses "relax" continually

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“…For more general problems, a method in which the hereditary integral form is reduced to a set of Volterra integral equations, was outlined. Narayanaswamy and Gardon [5] showed that the trapezoidal rule was used by Lee et al to approximate the integrals results in large errors when the kernel is strongly nonlinear, and proposed a modified integration scheme in which the integral is evaluated with respect to the pseudotime instead of the actual time. This scheme takes advantage of the smaller variations of the kernel function with respect to the pseudotime.…”

Section: Introductionmentioning

confidence: 99%

Numerical prediction of process-induced residual stresses in glass bulb panel

et al. 2006

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A numerical simulation model for predicting residual stresses which arise during the solidification process of pressed glass bulb panel was developed. The solidification of a molten layer of glass between cooled parallel plates was used to model the mechanics of the buildup of residual stresses in the forming process. A thermorheologically simple thermoviscoelastic model was assumed for the material. The finite element method employed was based on the theory of shells as an assembly of flat elements. This approach calculates residual stresses layer by layer like a truly three-dimensional calculation, which is well suited for thin pressed products of complex shape. An experimental comparison was employed to verify the proposed models and methods.

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Calculation of Residual Stresses in Glass

Cited by 105 publications

References 3 publications

Thermal-tempering analysis of bulk metallic glass plates using an instant-freezing model

Thermal-tempering analysis of bulk metallic glass plates using an instant-freezing model

Modeling and simulation of residual stresses during glass bulb pressing process

Numerical prediction of process-induced residual stresses in glass bulb panel

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