Thickness Stresses

Abstract

Residual stresses in a glass sheet occur due to the temperature gradient during cooling across the transformation range. It is customary to consider that these stresses are the result of superposition of two kinds of stresses: thickness stresses and membrane stresses. The former are generated by the temperature gradient which is perpendicular to the surfaces and the latter is generated by the gradient parallel to the surfaces. When a glass sheet gets cold during tempering or annealing, the heat transfer occurs principally through its surfaces. Consequently, the highest temperature gradient is directed across the sheet thickness and the main residual stresses are the thickness stresses. They are planar stresses. If we refer to an orthogonal system of axes Oxyz, with Oz perpendicular to the surfaces, we may write

$$ {\sigma _{x}} = {\sigma _{y}} = f(z),\;{\sigma _{z}} = 0 $$

((8.1))

.