温度・粘度
Thickness-Squared Cooling Rule
Japanese: 厚み二乗冷却則
A fundamental rule of cooling design states that the permissible cooling rate is inversely proportional to the square of the thickness (q ∝ 1/t²). If the thickness doubles, the cooling rate must be reduced to one-fourth.
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The Adams-Williamson rule (Adams & Williamson 1920) is a theoretical rule that states the permissible cooling rate q [K/min] of glass is inversely proportional to the square of the plate thickness t [mm], i.e., q ∝ 1/t² (treatise §4.2). Intuitively, glass that is twice as thick must be cooled at one-fourth the rate to limit residual stress to the same level. This relationship is derived from the thermal diffusivity κ and the stress-optical coefficient C of glass; it indicates that while rapid cooling is permissible for thin glass (flat plates), the cooling time must be extended more rapidly as the thickness increases.
Bullseye Glass has published the “Annealing Thick Slabs Chart ([R2], Bullseye 2017), which integrates these theoretical principles with field measurements. It specifies concrete permissible cooling rates of 83°C/h for 6 mm thickness, 27°C/h for 19 mm, and 4°C/h for 50 mm. Since the effective thickness in actual pieces varies depending on the shape and the uniformity of the furnace temperature, it is safer to use settings that are stricter than those derived from a simple flat-plate conversion (effective thickness correction). The author (Rei Chikaoka) has reported multiple cases—based on strain inspections using actual polarizing plates made from OYF’s proprietary alloys—where the glass was finished without cracking even within time frames shorter than those predicted by the Adams-Williamson rule, suggesting that differences in stress relaxation rates may be due to variations in the alloy composition.
Related Concepts
熱衝撃割れ（thermal-shock-fracture）・歪点以下破壊（sub-strain-fracture）・実効厚み（effective-thickness）・偏光板テスト（polariscope-test）・ランプ（ramp）・OYFガラス（oyf-glass）
This entry is written in Japanese by Rei Chikaoka and translated for readers outside Japan. If something reads oddly, the original is the source of truth.