This was a lecture given by Dan M Watson to a glass conference in Wagga Wagga, Australia 1999. Dan was a member of the Steward Observatory Mirror Lab team in Tucson Arizona.
At the Steward Observatory Mirror Lab we cast very large mirror blanks by melting chunks of borosilicate glass into a complex mold. The glass we use is called E-6, from Ohara Inc. of Japan, and is much like the familiar “Pyrex” glass from Corning Corporation. The current blank is 8.4 meters (27.6 Feet) in diameter, a meter thick at the edge, and has a cast weight of about 42,000 lbs (19,050 kgs). We have to anneal our castings to assure a very low residual stress and we must measure and document these stresses. We have adopted a simple and practical approach to annealing that is easy to understand and to practice. It is this measurement-based approach that I wish to share with you.
Annealing is the process of cooling glass through a certain temperature range at a rate that leaves the desired amount of residual stress in the piece. The top of the annealing range is the “Anneal Point”. The anneal point is defined as that temperature at which the viscosity (1013poises) of the glass will allow any induced stress to relax out to a negligible amount in just a few minutes. The bottom of the anneal range is a temperature a little below the “Strain Point”. The strain point is defined as that temperature at which the viscosity (1014.5 poises) allows the same stress relaxation in four hours. The strain point is usually about 50oC (90oF) below the anneal point. These temperatures are normally obtained from the manufacturer’s literature. Throughout this paper I will use degrees Centigrade versus degrees Fahrenheit and refer to XX degrees C simply as XX C for brevity.
Over the last few years I have had the opportunity to talk to a number of glass artists about their work and have been interested in their approach to annealing. Often they seem a little vague on the subject and somewhat haphazard in its practice. One glassblower (who shall remain nameless) cheerfully showed me his annealer’s clever controller made from a can attached to a rheostat. He wrapped string around the can, put a weight on the string, then adjusted a strap that that rubbed on the can to provide just enough friction that the weight would slowly slip down, turning the can and heat down as it went. To change the cooling rate, he just adjusted the friction on the can! Clever as it was, I suspect it may have been a bit unreliable. Many artists rely on old annealing schedules obtained years ago in graduate school or from some other glass worker and they may not really know if those schedules are appropriate for their current conditions.
There are useful guides to annealing available in the scientific and industrial literature but the math can be obscure and they are often tailored to very specific circumstances. For general treatments and assorted tables written for the glass artist one can read Boyce Lundstrom’s Glass Fusing” books, or Bandhu Scott Durham’s ”Contemporary Lampworking”. Dan Schwoerer’s recent technical article in the G.A.S Newsletter also provides a compact table of time and temperatures for annealing. Henry Halem’s “Glass Notes” has several techniques and schedules of interest. Any of these may help one establish an approximate schedule that can then be adjusted to fit the particular conditions. Unfortunately, all these tables have some assumptions factored in and the author may not explicitly state what they are. For example, if the chart calls for a certain rate for ½” thick glass is that for glass exposed to air on all sides, or cooling from one side only, or encased in a mold? If one’s work is not an even thickness, what number from the tables does one use? There are many factors that influence the way the glass cools and tables can be misleading. In many cases, annealing by rules and tables will cause the artist to spend more time cooling than is necessary, wasting time and money.
It seems that a big source of confusion in many people’s minds is the difference between annealing (which is simple), and heat transfer within the complex system of glass, mold or form, other thermal mass in the furnace and the geometry and heat loss characteristics of the furnace itself.
Although annealing is accomplished through the heat transfer, let’s look at it separately for clarity. Besides, annealing is the easy part. It only requires one simple equation.
The residual stress (s) in pounds per square inch (psi) left in your piece after cooling will be:
s = E. α. dT
Where E is Young’s modulus in pounds per square inch x 106, α (alpha) is the coefficient of thermal expansion x 10-6 and dT or ΔT is the measured temperature difference between the warmest and coolest parts of the glass as it cools through the annealing range. (E and alpha are usually obtained from the manufacturer). This equation is linear, (ie has no exponential terms) so if you halve your dT, the resultant stress is halved as well. The relationship of dT to steady-state cooling rate is similar. If you halve the number of degrees/minute of cooling, reduce dT by half.
Any difference in temperature in a piece of glass will induce a thermal stress, but at temperatures above the anneal point the glass can”give” and the stress relaxes out immediately. The viscosity of glass at the anneal point is such that any stress arising from the temperature difference dT can relax to nearly nothing in just a few minutes. The viscosity increases rapidly as you cool, until at the strain point the same stress takes four hours to relax. As you cool below the strain point, stress cannot relax in time and is effectively frozen into the piece. When the glass reaches room temperature and achieves thermal equilibrium a permanent residual stress forms that is equal in magnitude but opposite in sign to the stress from the dT during annealing. While glass cools through the anneal range the outside surface will be cooler than the interior. It will be in tension and the inside will be in compression. As the glass reaches equilibrium at room temperature a residual stress will be formed that has the same magnitude and “shape” as the thermal stress during annealing but the outside will now be in compression and the inside in tension.
There are situations where residual stress may be desirable, (eg in products like tempered glass) but for art glass we usually want the residual stress to be as small as is practical.
In practice, one decides how much stress they can accept in the finished piece, plug the numbers for the glass you are using into the equation above, then solve for dT. This dT dictates how fast to cool. A very good anneal will leave less than 100 psi of stress. Residual stress can become dangerous as they approach and exceed the 1000 psi range. Bear in mind that any residual stress from annealing may add to stress caused by other conditions such as thermal expansion mismatch of materials. All of the internal stresses may be magnified and concentrated by the shape and weight distribution of the piece as well. A residual stress as low as possible given practical and economical limits is usually the goal and typically you’ll be shooting for a maximum dT of at most a few degrees C. Table 1 shows dT computed for 100 psi residual stress for some common glasses.
dT = 100 psi / E x α
If we want to achieve a residual stress of 100 psi in the glass, we need to cool through the annealing range (from the anneal point Tg to about Tg-50C) at a rate that produces a temperature difference (dT) between the warmest and coolest part of the glass piece of no more than the following:
|Glass type||Young’ modulus||α||dT||Anneal point Tg.|
|Gaffer Crystal||8.27 x 106 psi||9.2 x 10-6||1.31 C||430 C|
|Schott F2||8.27 x 106||9.2 x 10-6||1.31 C||430 C|
|Scott LF5||8.55 x 106||10.6 x 10-6||1.10 C||411 C|
|Spruce Pine 87||9.5 x 106||9.65 x 10-6||1.09 C||477 C|
|Bullseye 1101||10.0 x 106||9.0 x 10-6||1.11 C||516 C|
|Corning Pyrex||9.1 x 106||3.25 x 10-6||3.38 C||560 C|
|Ohara E6||8.33 x 106||2.5 x 10-6||4.80 C||540 C|
|Bottle glass||10.0 x 106||8.5 x 10-6||1.18 C||533 C|
For our latest casting (at the Mirror Lab), we wanted a residual stress of about 30 psi. This dictated a dT of about 1.5 C. We actually decided to keep dT less than 1 C to be safe. We scheduled the furnace to cool from high temperature of 1180 C like this:
|Degrees C||@ C/hour|
|1180 -1000 C||-25 C/hr|
|1000 - 650||-10.4|
|650 – 630||-1.7|
|530 - 450||-0.104 (anneal point of E-6 =540 C (32 days at this step)|
|450 – 400||-0.208|
|400 – 271||-0.5|
|271 – 210||-0.42|
|210 – 120||-0.33|
|120 – ambient we let it freefall|
With a week to heat to high temperature, this schedule required a total elapsed time of about 90 days. This is for low expansion glass and a lightweight, hollow structure; a solid blank would take much longer. Below the anneal range we did not want the temporary stress to be more than 8 times the permanent stress from annealing, so the changing rape rates below 450 C approximate a natural exponential cooling curve that results in a dT of no more than 8 C.
Most artists don’t need to be quite so patient (and I do not advocate that anyone try to use the above schedule), but the technique is universal. The basic steps are the same for any annealing problem; only the scale changes.
Heat Transfer is not simple and can be hard to calculate. Glass artists use a broad variety of materials, techniques and equipment. Small changes in an annealer’s insulation can make a relatively large change in temperature profile within. The mass and insulating characteristics of molds and forms can drastically alter the heat transfer through the glass. In theory, one could factor all of these into the calculations and adjust the rates accordingly, but that can be difficult and unreliable. By far the best way to assure a desired dT is to measure it! No amount of theory can produce as sure a result as a few simple measurements.
The Mirror Lab’s large spinning furnace has over 500 thermocouples (TCs for short) measuring every possible significant area, including 30 inside the mold’s interior at strategic places. However, I use the same technique to anneal samples in an 8” test furnace with only two TCs. The simplest technique is to measure the air temperature in the annealer and have a thermocouple at a point that is certain to be at least as hot as the warmest part of the glass. The difference between these measurements will be a good conservative value for dT. If your piece is large or complicated it’s a good idea to use a number of TCs to measure any questionable areas. An investment in thermocouples and a way to read them is the best way to guarantee a quality anneal. Most of you probably use some type of controller with a TC reading air temperature so you are already halfway there. One or more additional TCs can be read periodically and all the temperatures recorded on a graph of time vs. temperature. (Coloured pencils drawn on graph paper is a technique that served us well for years before we were blessed with computers). As you cool at any constant ramp rate the lines will become parallel and a vertical line drawn through them will display the effective dT. The resulting graph makes an excellent document for your records and valuable reference in the future.
On the subject of thermocouples, I must state that one important point. Never trust one TC alone, especially type K. K type TCs will develop errors as they are subjected to temperatures much above the annealing range. All TCs can suffer invisible damage and ageing that can cause them to indicate the wronf temperature, or to indicate the temperature at some place other than the tip. I have seen many cases where a single K TC is used to control a kiln or annealer and it may not be tested or checked until it fails altogether. When compared to a known reference TC, these are often in error, sometimes by many degrees. If one has several TCs on hand, they can be compared to one another and the worst ones identified (and destroyed). The best practice is to buy or make a number of identical TCs and keep at least one of them as a reference. If that reference TC is never heated above annealing temperature it will be fairly reliable. Modern digital TC readers are very accurate and easy to use and the prices are falling to the point that every studio can afford one. The small handheld units are especially useful. Older analog types (known as galvanometric pyrometers) are prone to several types of problems and are not recommended.
In most cases one can easily arrange to have a TC positioned to be a little warmer than the glass during annealing. In most cases the glass loses its heat to air, because the floor of the annealer is relatively well insulated. Most mold materials are relatively insulating as well. One simple technique is to slip a TC into a groove cut into a piece of fiberboard or dense blanket, then set the work to be annealed over the tip of the TC. Normally the bottom of a work is its thickest part, so the TC will stay warmer than the glass as the annealer cools. If one is casting, fusing, or slumping, a TC can be incorporated into the mold or form by inserting it into a hole or investing it directly. If one makes works that are similar size and mass, then only one piece in the annealer need be measured. If the work is varied, the largest of the thickest piece will be a conservative choice to measure. If one’s annealer is not thermally homogenous, then measuring near the worst heat leaks (usually the corners around the door edges) will be conservative.
A very useful way technique is to make ”dummy” or witness samples, that are blocks or cylinders of the same glass as that being annealed. Choose blocks that are a little thicker than the work to be annealed and drill holes into them for TCs. These can be arranged to simulate the work’s thermal environment and act as a surrogate to measure. For critical annealing jobs, the residual stress in these witness samples can be measured and they can be saved for your records. If one’s work is opaque or darkly coloured, then a transparent witness sample is especially useful for later stress analysis.
This measurement-based technique is a practical application of classical annealing. Of course life is really not that simple. Every thing that the artist does to glass can change it. Mixing colours and layering glass creates a composite of properties that may not be well described by the manufacturer’s specifications. Differences in the viscosity or other properties of the various components introduce complications that are hard to predict. These complications are outside the scope of this of this current article, but can be a source of problems which cannot be relieved by any annealing technique.
Because every annealer-mold-glass combination is unique, it can be difficult to calculate what the best annealing rate should be. Tables and “rules of thumb” may not be accurate for an artist’s unique circumstances. With simple and practical measurement, you can assure the best possible anneal every time.