Session: 11-46-01: Methods and Algorithms in Computational Heat Transfer

Paper Number: 95742

95742 - Investigation of Thermal Stresses in Glass During Manufacture 

Abstract

Glass is manufactured in a three-part operation: the batch house, the hot end, and the cold end. The batch house prepares the raw ingredients, the hot end melts and forms the glass, and the cold end cools and anneals it. Internal stress is created when one surface of a glass pane or bottle is heated or cooled. Thermal stresses caused by manufacturing processes, as well as minor glass defects such as air bubbles and micro cracks, reduce the fracture toughness of the glass. If  the stress reaches a critical value that depends on several factors, the glass will crack. Determining the magnitude of thermally induced stresses during manufacture is essential in order to prevent failure. 

Glass is stronger in compression than tension. Cooling one side of a hot glass plate causes tension on that side and compression on the opposite side. Because defects are less sensitive to compression than tension,  reaction to the presence a bubble or scratch depends on whether the defect is on the heated side or the cooled side. For maximum process efficiency, rapid cooling is required, but the cooling rate is limited by the cooling agent used (air cool versus liquid spray) and the allowable thermal stress. The total strain will be a combination of the load-induced strain and the thermal strain which its determination requires solution of the related transient heat flow problem. The corresponding stresses will be used to compute the vonMises stress and the maximum shear stress in the glass. Two criteria will be used to assess the failure:

1. The Maximum Distortion Energy Criterion (MDEC) or the vonMises criterion according to which
failure or yielding occurs at a point in the glass when the distortion strain energy per unit volume reaches the limiting distortion energy per unit volume as determined from the tension test.

2. The Maximum Shear Stress Criterion (MSSC) or the Tresca criterion which  states that failure will occur when the maximum shear stress reaches the maximum allowable stress which is half of the  yield strength. 

A mathematical model for the temperature field and the thermal stresses in glass during manufacture is presented. The finite difference method (FDM) is used to solve the governing equations and a MATLAB program is used to carry out calculations. The method will be applied to both flat glass sheets and bottles. The simplicity and flexibility of this method combined with minimal computational effort makes it an ideal approach compared to using commercial tools like the finite element method.

 

Presenting Author: Enayat Mahajerin Saginaw Valley State Univ

Presenting Author Biography: Enayat Mahajerin is a professor of Mechanical Engineering at Saginaw Valley State University (SVSU). <br/>His research interests are Applied Mathematics, Computational Mechanics, Solid Mechanics and Structural Failure Analysis. He received his Ph.D. in Engineering Mechanics from Michigan State University (MSU) in 1981. He is a Fellow of the American Society of Mechanical Engineers (ASME).

Authors:

Enayat Mahajerin Saginaw Valley State Univ