Glass viscosity changes by about a billion-fold between the annealing point and the working range, and the curve is steepest at the cool end where the glass is invisible to the eye. A viscosity near 10^4 dPa·s is the working point, 10^13 dPa·s is the annealing point and 10^14.5 dPa·s is the strain point, below which stress takes about 18 minutes to relax by a factor of e and cooling can safely speed up. This is why a blower has seconds at the pipe but the lehr must be controlled for hours.
Part of Glass Blowing and Forming
The relationship between temperature and how stiff glass is, and the arithmetic behind the working, annealing and cooling rules of thumb.
Viscosity Falls Steeply And Not In A Straight Line
Viscosity is resistance to flow. Honey is around 10 Pa·s; pitch is around 10^8 Pa·s; glass at the annealing point is about 10^12 Pa·s. Glass-technology references quote viscosity in poise or dPa·s (the same unit: 1 dPa·s = 0.1 Pa·s) and define a handful of fixed points on the curve. This article uses those standard definitions; the figures are textbook values from the glass-science literature, not from a line in this corpus, and the corpus’s own temperature table is quoted beside them.
| Fixed point | Viscosity (dPa·s) | What it means at the bench |
|---|---|---|
| Working point | about 10^4 | Gathers and blows freely |
| Softening point | about 10^7.6 | Slumps under its own weight |
| Annealing point | 10^13 | Internal stress relaxes in minutes |
| Strain point | 10^14.5 | Stress no longer relaxes in practical time |
Plotted as log viscosity against temperature, the curve bends: each degree removes more viscosity at the cool end than at the hot end. The consequence is that a small error in oven temperature costs far more near the annealing point than the same error in the glory hole.
What You Need
- The carrier article’s temperature table: soda-lime working range 900-1,050 °C, softening 700 °C and annealing 510 °C.
- A thermometer that reads 500 °C. Without one, none of this arithmetic can be applied; see Annealing Oven.
Method: Turn The Curve Into Bench Rules
Step 1: Count the decades. From the working point (10^4) to the annealing point (10^13) is 13 − 4 = 9 decades, a factor of 10^9.
Step 2: Average the slope. Using the middle of the soda-lime working range (900 and 1,050 give 975 °C) and the 510 °C annealing temperature, the span is 975 − 510 = 465 °C. Nine decades over 465 °C is 465 ÷ 9 ≈ 52 °C per decade. That is an average; because the curve steepens, the true figure near 510 °C is smaller, so a 50 °C error in the lehr changes viscosity by at least a factor of ten.
Step 3: Convert viscosity to relaxation time. A rough stress relaxation time is viscosity divided by shear modulus. Take soda-lime shear modulus as about 30 GPa (3 × 10^10 Pa, recalled, not from the corpus).
- At the annealing point: 10^13 dPa·s = 10^12 Pa·s, so time = 10^12 ÷ 3 × 10^10 ≈ 33 seconds.
- At the strain point: 10^14.5 dPa·s = 10^13.5 Pa·s ≈ 3.2 × 10^13 Pa·s, so time ≈ 3.2 × 10^13 ÷ 3 × 10^10 ≈ 1,070 seconds, about 18 minutes.
The strain point is 31.6 times more viscous than the annealing point (10^1.5), and the relaxation time rises by the same factor.
Step 4: Read the cooling rule. Between the annealing point and the strain point stress relaxes in 33 seconds to 18 minutes by the estimate above, so cooling must be slow enough to let it. Below it, relaxation is so slow that stress is effectively frozen in, so the rate only needs to be slow enough to avoid new thermal gradients. This is the logic behind the carrier’s instruction to hold at the annealing temperature, cool at the stated rate to 100 °C below, and then allow faster cooling.
Worked Example
Soda-lime at the carrier’s 2 °C/min: from 510 °C to 410 °C takes 100 ÷ 2 = 50 minutes. Borosilicate at 1 °C/min from 560 °C to 460 °C takes 100 ÷ 1 = 100 minutes. The carrier gives total times of 3-4 hours and 5-6 hours for a 5 mm wall, which include the 30-minute hold and the faster tail. The Annealing article gives a slower 0.5-1.5 °C/min through the strain point for 6 mm soda-lime; the two are not reconciled in the corpus, and slower is the safe direction.
Common Mistakes
- Using colour at the annealing point. There is none; see the danger block below.
- Assuming a 10 °C thermometer error is harmless. At roughly 52 °C per decade on average, 10 °C is about a 1.6-fold viscosity change, and more near 510 °C.
- Extrapolating the table linearly between rows. The curve is not a straight line; interpolating from three points is a guide, not a prediction.
Safety
The steep part of the curve is the part you cannot see
Viscosity is changing fastest between roughly 600 °C and 510 °C, and glass glows only above about 600 °C. A piece cooling through that range looks cold and burns at once. Treat anything that has been in the furnace as hot until the oven reads room temperature.
What’s Next
- Learn next: Annealing Oven (Lehr) — building the chamber that applies these rates
- Combine with: Stress Testing — checking whether the schedule worked