Wire in glass

 

The cracks around the wire imbedded in the glass in the above image are not incompatibility cracks. They do not surround the square piece that traps the wire into the glass. These are from differential expansion/contraction stress between the wire and the glass. 

 

Picture credit: Charmaine Maw

This picture shows the stress that a single strand of wire will induce in glass (the bright light around the wire).  Wire is never going to have similar characteristics to the glass, so the glass must be strong enough to contain the resulting stress.  Anything that increases the mass of the wire, such as twisting or spirals, will increase the stress. 

 

Kanthal and nichrome wires are best as included wire hangers. They are designed for high temperature work and so do not weaken from the heat. This means that high temperature wire as thin as 0.5mm/22 gauge can hold a lot of weight.  Much greater weight than is used in most glass objects to be hung rather than fixed.

Keep the wire as a single strand and as thin as possible, consistent with sufficient strength.  Hammering wire flat can also help reduce the stress by thinning it.

Profile

A sharp tacked piece needs to be fired as though thicker. This example is a single layer base and a square of glass to trap the wire fired to a sharp tack.  It needs to be fired as though 2.5 times the thickest part - 15mm.  A rounded tack fuse of the same layup would need to be fired as for 12mm.

Layup

The use of wire in glass needs to consider how the air will escape from around the wire.  Yes, if the wire exits the glass, there is a channel for it to dissipate.  But air tends to collect along the length of the wire.  If the wire is fully enclosed in the glass, the layup must accommodate the need for air escape routes.  This might be with a fine layer of powder, design elements, chips of glass to hold the outer edges of the glass up for longer, or other devices.

 

Scheduling

The example shown at the start of this blog, is a sharp tack and needed the 2.5 times scheduling.  That probably would have avoided the crack in the single layer base.  That single layer cools faster than the wire with the added piece of glass.  A bubble squeeze is a good idea, even though it would not normally be considered.  This gives the best chance of reducing the bubbles that form around the inclusion.

 

You need to be careful about increasing the ramp rate until the glass has passed out of the brittle phase.  This is about 540˚C/1005˚F. The increase in the ramp rate during the brittle phase may cause cracks. It is, of course, more likely to occur during cooling because the metal will be contracting more than the glass during the brittle phase.  This contrast in contraction rates induces stress that may be great enough to crack or break the glass.

 

 

Slow Rates to Annealing

"I have seen recommendations for slower than ASAP rates from the top temperature, but most schedules say 9999 or ASAP.  Which is right?"

Slow drops in temperature from top to annealing temperatures risk devitrification. Accepted advice is to go ASAP to annealing temperature to avoid devitrification forming.

Breaks do not occur because of a too rapid drop from top temperature to annealing. The glass is too plastic until the strain point has been passed to be brittle enough to break. On the way down that will be below an air temperature of 500˚C/933˚F.

credit: ww.protolabs.com

Different kilns cool from top temperature at different rates. Ceramic kilns are designed to cool more slowly and may need assistance to cool quickly.  This is usually by opening vents or even the door or lid a little. Glass kilns are designed to lose temperature relatively quickly from high temperatures. They do not need a crash cooling as ceramic kilns may need in certain circumstances.  Of course, crash cooling may be necessary for some free drops and drapes.

The length of the soak at annealing is determined by the effective thickness of the piece.  Tack fusing needs to be annealed for thickness as a factor of 1.5 to 2.5, depending on profile.

The extent to which you control the cooling to room temperature after the anneal soak is dependent on the calculated thickness of the piece you are cooling. The objective is to keep the internal temperature differential to 5˚C/10˚F or less to avoid expansion/ contraction differences that are great enough to break the piece. Those rates are directly related to the required length of the anneal soak.  Those rates can be taken from the Bullseye chart for Annealing Thick Slabs. The Fahrenheit version is is available too.

An example.  If you have a 2 layer base with 3 layers (=15mm) stacked on top for a rounded tack fuse, you need to fire as for at least 30mm. This will require controlled cooling all the way to room temperature.

• ·        The rate to 427˚C /800˚F will be19˚C /34˚F
• ·        The rate to 370˚C /700˚F will be 36˚C /65˚F
• ·        The final rate 120˚C /216˚F to room temperature.

You may need to wait a day before any coldworking. An example from my experience shows the necessity.  I checked a piece for stress a few hours after removing the piece from the kiln when it felt cool to the touch. It puzzled me that stress showed, although it didn't on similar pieces.  The next morning, I went to check if I misunderstood the reading. Now, a full 15 hours after coming out of the kiln, there was no stress.  The example shows that the glass internally is hotter than we think. And certainly, hotter than the air temperature.

In the temperature regions above the strain point, the glass needs to be cooled quickly. In the annealing region and below the glass needs to be cooled slowly.

More information is available in the eBook Low temperature Kilnforming.  This is available from Bullseye or Etsy

Identification of Mechanical and Thermal Stress

The Identification of stress is important in investigating the causes of stress. We have well established clues to help us with our glass selection and alteration of our firing schedules. We can get more information about why the cold glass has broken from the scientific literature. The manufacturers of float glass and the installers of large panes investigate thoroughly the causes of breaks in glass that has been installed. 

One article - Breaking It Down, Why Did the Glass Break? by Timothy Bellovary from Vitro Architectural Glass - looks at mechanical and thermal stress and distinguishing between the two.  This post is quoted extracts from that article. [Text in square brackets are interpolations of mine].   Note that all the illustrations are from the article and are copyrighted.

Source: https://vcn.vitroglazings.com/technical-forumdiagnosing-glass-breakage

Identifying the break origin can provide hints about the following:

·         Mode of glass failure—Was it mechanical or thermally induced stress?

·         The stress or tension level at which the breakage occurred.

·         Other contributing factors—were there digs (deep, short scratches) resulting from glass-to-glass or glass-to-metal contact? Did a projectile hit the glass? Is there edge or surface damage?

 

To find the origin of a break, the first step is to assess its direction by inspecting the fracture lines… in the glass. These rib-shaped marks, distinguished by a wave-like pattern, begin at the break origin and radiate along break branches, and almost always project into the concave face of these lines.

Figure 1
Diagram of Fracture Line Direction

It’s often helpful to make a basic diagram (see Figure 1) of the fracture lines. … The origin of the break can be determined by:

·         Drawing arrows (indicating fracture line direction) pointing into the concave face of break wave markings in the glass edge.

·         Tracing point-to-tail of arrows back to the break origin.

 

Mechanical Stress

Low-stress tension breaks are experienced most frequently by residential window and IGU manufacturers. The origin of the break is typically at damaged areas of the edge or surfaces near the edge, such as digs, scratches or chips. In many cases, breakage from damaged glass occurs after the initial edge damage is incurred, such as during IGU fabrication, sashing operations, transportation, job-site handling or storage, or the installation process.

In Figure 2, the break origin is not 90 degrees to the edge of the glass, indicating a tension break caused by bending. Low-stress, mechanical tension breaks often occur from bending at less than 1,500 psi.

Figure 2

Low-Stress Mechanical Tension Break

High-stress tension breaks share one characteristic with low-stress tension breaks: The break origin is not 90 degrees to the edge of the glass, suggesting a tension break caused by bending. However, additional branching of the crack within two inches of the break origin (see Figure 3) indicates that the stress at breakage was likely higher than 1,500 psi.

…

Figure 3

High-Stress Mechanical Tension Break

 

Thermal Stress

Thermal stress breaks often originate at the edge of the glass and form virtually 90-degree angles to the edge and surface of the glass.

As with mechanical stress, there are two types of thermal stress breaks: low stress and high stress.

 

Figure 4

Low-Stress Thermal Break

Low-stress thermal breaks are often indicated by a single break line starting at the break origin point at or near the glass edge and propagating two inches or more before branching into more break lines (see Figure 4). Damaged glass edges are the most frequent cause of low-stress thermal breakage.

 

High-stress thermal breaks appear as a single break line starting at the break origin point at or near the glass edge and generally branching into additional breaks within two inches [50mm] of the origin. This indicates a breakage brought on by conditions that cause high thermal stress, such as severe outdoor shading on parts of the glazing; heating registers located between the glass and indoor shading devices; closed, light-colored drapes located close to the glass; or glazing in massive concrete, stone or similar framing.

Figure 5

High-Stress Thermal Break

Analysing the Break Origin

A reliable method for estimating the stress level of a break at failure is a mirror radius measurement. Radius dimensions are determined by crack propagation velocity characteristics.

A crack propagates itself through glass with increasing velocity as it moves further from the point of origin. If an object has sufficient energy to propagate a crack through the thickness of the glass, then a “spider web” pattern will form. ….

Near the point of origin, a smooth, mirror-like appearance on the fracture face indicates a low crack velocity. However, as velocity increases (due to higher tension stress), the fracture face takes on a frosted look; then, at the highest velocity, it assumes a ragged or hackled appearance. Mirror radii appear in various forms, depending on the stress level of the fracture.

Figure 6 shows break origins resulting from high tensile stresses, such as bending or thermal stress breaks.

Figure 6

High-Stress Mirror Radii
(R = Mirror radii)

 

Figure 7 represents the break origins of glass fracturing at low bending stresses. In this example, a smooth fracture face forms across the thickness of the substrate. When the breaking stress is low, the mirror radius is often radial and may extend deeply into the substrate.

Figure 7

Low-Stress Mirror Radii
(R = Mirror radii)

 

To identify what damaged the glass in the first place, four factors are examined during this analysis:

·         Impact

·         Inclusions

·         Thermal variance

·         Pressure differentials

Impact

Identifying the nature of the breakage pattern can determine whether a foreign object hit the glass and whether the impact was perpendicular or parallel.

Depending on the severity of the impact, the immediate area surrounding the break origin might be cracked, crushed or missing.

                 

Figure 9

High-Stress Mechanical Breakage

[This pattern of break is often exhibited when the separator fails or is insufficient to keep the glass from sticking to the ceramic support shelf.] …

Inclusions

Any undesirable material embedded in glass is considered an inclusion. ... [In general, kilnformers place inclusions within the glass and know the risks of breaks].

Thermal Variance

[This article relates to float glass installations, but the principle remains.] If the temperature difference across a [piece] of glass is great enough, the accompanying stresses can reach levels that cause breakage. … The combination of contact, surface damage and localized temperature gradients can greatly increase the likelihood of breakage.

Pressure Differentials

[This section applies mainly to Insulated Glazing Units. It points out that differences in altitude between the manufacturing and installation sites – in combination with temperature – can cause breaks. It is not of primary importance to most kilnforming, but something which should be considered when installing kilnformed glass in an IGU]

Conclusion

[Occasionally] glass breaks for no obvious reason. Whether it’s a one-off or part of a continuing pattern of incidents, glass breakage is inconvenient, potentially dangerous and costly. … Conducting “post-mortems” on glass breaks helps investigators identify the general reasons for each incident, including the type of failure that caused the break, and the potential original source of the damage. By using the techniques outlined in this article, [kilnformers] may be able to accurately identify the likely origin of such failures and … use that information to prevent future occurrences.

https://vcn.vitroglazings.com/technical-forumdiagnosing-glass-breakage

[An important element in identifying breaks in kilnforming that this article demonstrates is the difference in the angle of the break. A 90 degree angle to the surface indicates a thermal cause to the break. The more branching of the lines of breakage, the greater the stress. The branching breaks indicate there was significant temperature difference.

The breaks which are less than a right angle to the surface indicate a mechanical origin of the stress. This is usually the glass breaking at a weak point when subject to a bending stress.

If the point of origin of the stress can be identified as demonstrated in the article, it may help in determining causes. One of these causes might be hot or cold spots in the kiln.]

 

 

Inadequate Annealing - Effects on Next Firing

Credit:

https://immermanglass.com/about-kilnforming/cracks/

The speculation about breaks caused by inadequate annealing of the piece on the previous firing is common.  I do not know if this can be proved to be inaccurate, but we should think about it.

A parallel condition to this poor annealing is toughened/tempered glass which is under a lot of stress between the inside and outside surface of the glass. As Bob Leatherbarrow mentioned to me, we can heat up the highly stressed toughened glass without breaking it by using moderate ramp rates. During this heat up in the brittle phase, the stress is gradually relieved. It does require the moderate ramp rates, of course. 

This parallel circumstance of heating toughened/tempered glass which is highly stressed raises the question: Why should mildly stressed kilnformed glass suffer breakage, if fired at a reasonable rate? Highly stressed toughened/tempered glass does not.

If we apply the experience of relieving the stress in toughened/tempered glass, you can see how inadequately annealed glass behaves. The under-annealed glass has stress distributed (possibly unevenly) across its substance. As the glass temperature moves toward the strain point it becomes less brittle and the stresses are reduced. By the time the glass reaches the strain point, the stresses from poor annealing are relieved.

Any glass not fired slowly enough for its thickness or layup toward 300˚C/573˚F will break. This has been observed to occur around 260˚C/500˚F.  This most commonly occurs in pieces that are laid up with different thicknesses  across the surface. The heat cannot reach the bottom layers as quickly as the overlying ones. The expansion of covered and uncovered glass - due to the heat exposure - is to different.

Thinking about the behaviour of glass in this way indicates that breaks early in the firing relate to a too rapid ramp rate, not necessarily a previous annealing problem. We should, of course, be checking on the stress in our pieces after each firing. This will alert us to the amount of stress in the piece and so to be more cautious in the ramp rate and in the annealing during the current firing. 

Speculation about inadequate annealing in a previous firing as a cause of breaks is misplaced. The thinking that stress will carry through the heat-up and cause breakage is misdirected. 

More information on this is available in the eBook LowTemperature Kilnforming, an Evidence-Based Approach to Scheduling at Etsy VerrierStudio shop and from Bullseye Ebooks.

Kilnforming with 3mm Glass

 A power point presentation I made a few months ago to the group Lunch with a Glass Artist.

It is 33 slides long.

Kilnforming with 3mm Glass.pptx

Compatibility of Glasses with the Same CoE

Questions such as “How compatible are Wissmach W90 and Bullseye?” are asked from time to time.  This does show some awareness that Bullseye may not be Coe 90 and that CoE does not equal compatibility.  The same question may be asked about whether Youghiogheny Y96, Wissmach W96 and Oceanside are compatible with each other.

What is CoE

It is important to know what CoE means before the question can be answered.  It is a measure of average expansion from 20°C to 300°C.  This is suitable for crystalline materials as their low temperature expansion rates can be projected onto the behaviour of the material until near molten temperatures.  However, it is not suitable for non-crystalline materials, such as plastics or glass, as their behaviour is much more unpredictable as the temperature rises.  Measurementsof CoE have been made of glass at the glass transition temperatures which show at least seven times greater expansion near the annealing temperature than at 300°C. 

An extended essay on compatibility written by Lani Mcgregor is here, 

and here

Compatibility Tests

The degree of compatibility is uncertain between different manufacturers.  Each manufacturer will take their own way toward balancing the viscosity with the CoE.  While they can say their glass has similar characteristics to another manufacturer’s glass, they cannot guarantee compatibility.

When using glass from different manufacturers together, the best advice is to test the glasses yourself for compatibility. Do this before you commit to the project.  Bullseye notes how they do their stress tests on the education section.  I have been unable to ascertain how other manufacturers test for compatibility within their range of fusing glasses.  Another simple method of testing for stress is here.

There are reports that W90 and Bullseye work together and others that say they don’t.  There are those that say the 96 CoEs work with Oceanside, and those who say they don’t. Testing for yourself is the only way to know what works.

Scale

It seems that combining different manufacturers’ glasses may work at smaller scales, but less well at larger.  Since very few people test for compatibility before, or after, when combining different manufacturer's glasses, they don't know whether their pieces are showing signs of stress. Just because the pieces do not break immediately does not mean they are compatible or stress free. 

Size, Shape and Quantity

You should also note that the relative sizes and shapes of the combined glasses effect the survivability (rather than compatibility) of the piece.

Shape

The shape of the main piece has an effect.  Circular or broad ovals can contain the stress much more easily than a long rectangle or a wedge-shaped piece.

The same applies to the pieces added.  Pointed pieces concentrate the stress more than rectangular ones.  The stress from circular additions are easier than rectangles for the base piece to hold.

Placing

Where you place the additions is important.  Anything placed near the edge of the base is more likely to cause enough stress that it can not be contained and so the piece breaks.

Mass

How much of another manufacturers’ glass are you putting on the base?  The bigger the area or the thicker the piece(s) the less well the base will be able to hold the stress before breaking.

Re-firing

A frequently asked question is “how many times can I re-fire my piece?”

This is difficult to answer as it relates to the kind of glass and the firing conditions.

Kind of glass

Float glass is prone to devitrification. This often begins to appear on the second firing. Some times it may be possible to get a second firing without it showing. Sandblasting the surface after getting devitrification will enable another firing at least.

Art glass is so variable that each piece needs to be tested.

Fusing glasses are formulated for at least two firings, and experience shows may be fired many of times. The number will depend on the colours and whether they are opalescent. Transparent colours on the cool side of the spectrum seem to accept more firings than the hot colours. Both of these accept more firings than opalescent glasses do.

Firing conditions

Temperature

The higher the temperature pieces are fired at, the fewer re-firings are possible. So if multiple firings are planned, you should do each firing at the lowest possible temperature to get your result. This may mean that you have relatively long soaks for each firing. The final firing can be the one where the temperature is taken to the highest point.

Annealing

You do have to be careful about the annealing of pieces which have been fired multiple times. A number of people recommend longer annealing soaks. However, I find that the standard anneal soak for the thickness is enough. What is required is cooling rates directly related to the anneal soak.  This is a three-stage cooling as described in the Bullseye chart Annealing Thick Slabs.  The slump firing can be annealed at  the standard. 

Slumping

In general, slumping is at a low enough temperature to avoid any creation of additional stress through glass changes at its plastic temperatures.  But any time you heat the glass to a temperature above the annealing point, you must anneal again at least as slowly as in the previous firing. Any thing faster puts the piece at risk of inadequate annealing.  Of course, having put all this work and kiln time into the piece, the safest is to use the cooling rate as for a piece one layer thicker.  My research has shown that this gives the least evidence of stress.

Testing

Testing for stress after each firing will be necessary to determine if there is an increase in the stress within the piece. In the early stages of multiple firings, you can slow the annealing and if that shows reduced stress, it will determine your previous annealing schedule was inadequate. When reducing the rate of annealing does not reduce the stress, it is time to stop firing this piece at fusing temperatures.

Revised 6 May 2023

Effect of AFAP Rates

 

 

This graph illustrates the effect of a rapid increase (500C/hr) in temperature on the glass.  The blue line represents the air temperature measured in the kiln.  The orange line represents the temperature between the glass and the shelf.  At an air temperature of 815°C, the temperature of the glass at its bottom is around 750°C.  This is a large difference, even though the glass is in the plastic range.  It means that the potential for stress induced by the firing rate is large.  The graph shows the temperature difference evens out during the annealing soak.

 The fast rise in temperature at the initial part of the firing where the glass is still brittle risks breakage.  The difference in temperature between the top and bottom of a 6mm piece of glass is shown to be 100°C plus throughout this initial phase up to 500°C.  Most breaks due to thermal shock occur before 300°C. This large temperature difference that occurs with rapid rates of advance risks breakage early in the firing.

 As an example, I took a piece out at 68°C to put another in.  During the time the kiln was open, the air temperature dropped to 21°C.  I filled the kiln and closed the lid and idly watched the temperature climb before switching the kiln on for another firing.  It took a bit more than two minutes for the thermocouple to reach 54°C with the eventual stable temperature being 58°C.  I had not been aware how long it takes the thermocouple to react to the change in temperature.  Yes, it takes a little time for the air temperature in the kiln to equalise with the mass of the kiln, but not two minutes.

 With a two-minute delay the recorded temperature can be significantly behind the actual air temperature.  For example, a rate of 500°C per hour is equal to 8.3°C (15°F) per minute or 16.6°C (30°F) overshoot of the programmed temperature. Even at 300°C it is a 10°C (18°F) overshoot.  This effect, added to the way the controller samples the temperatures, means the actual overshoot can be significant for the resulting glass appearance.

 This is just another small element in why moderate ramp rates can be helpful in providing consistent results for the glass.

 More importantly at top temperature, the surface will be fully formed while the bottom is only at a tack fuse temperature. This does have implications for the strength of the piece.  There will be an only tack fused structure through much of the piece, but a full fused structure at the surface.  The potential for breaking in further kilnforming or during use is high.

 In addition to the effects on the glass, there will be effects on the operation of the controller.  Controllers operate by comparing the instructions on firing rate with the air temperature recorded by the pyrometer.  In doing this the variances become smaller with time.  An AFAP firing does not give a lot of time for the controller to “learn” the firing curve.  So, the controller tends to overshoot the top temperature by some (variable) degree.  This makes it difficult to precisely control the outcome of the firing.

 There is some concern that the structure of the kiln will be affected by AFAP firings. This is a small risk.  The expansion and contraction of the kiln materials will occur whether quickly or more slowly.  It is not a major concern.  It is a concern for the glass, though.

 AFAP firings have potentially harmful effects on the structure of the fired glass leading to thermal shock and fragile completed pieces.

Notes on Polarised Light Filters

Polarised light filters are used to detect stress in a non-destructive testing method in kilnforming.  The use of the filters is described in this blog. To produce consistent reliable results, there are certain conditions.

 The light source needs to be diffused in such a way that it is even across the viewing area.  An intense, single point light makes it difficult to determine the relative intensity of apparent stress. Another tip is that you can use your phone or tablet as a source of diffused light and as the bottom filter.  It emits polarised light, meaning only a top filter is needed.

Stress halos from broken and fused bottles

 It is important that the glass being tested is of the same temperature throughout to get a meaningful result.  This was emphasised to me when I was running a series of tests. I got in a hurry to test for stress to be able to start the next trial quickly.  I began to notice inconsistencies in the amount of stress I recorded for results of the series of tests.  Going back to the stressed test pieces, showed different stress levels when they were cold from when they were warm.

 The conclusion is that the glass to be tested for stress must be the same temperature throughout.  Even if it is only slightly warm, the apparent stress will be exaggerated.  It may be that the testing can only be done 24 hours after removed from the kiln.

 Stress will be more evident at points and corners.  The light will be brighter at highly stressed points, and even at extreme stress exhibit a rainbow effect.  More generalised stress is evident in a lighter halo.

Stress points in a drawing square illustrating the concentrated stress at corners

 It is much more difficult to check for stress in opaque areas of a piece.  If there are transparent areas, the stress will show there, although the stress may originate in the opaque ones. To be aware of potential stress in the combination of opaque glass, strip tests must be conducted on samples of the glasses. 

 Remember to include an annealing test too, as the stress test does not distinguish the type of stress.  If the annealing test shows stress, the annealing was inadequate. It is of course, possible that the glass is stressed because of incompatibility.  But the only way to determine that is to fire another test with a longer soak at annealing.

Annealing Previously Fired Items

“Double the annealing soak time for each firing” and “Slow the rate of advance each time you fire” are common responses as a diagnosis when a piece breaks in the slumping process.  It may come from the fact that once fired, It is now a single piece that needs a slower rate of advance on the second firing.  I’m not sure where the idea of doubling the annealing process originates.

You need to think about why you would slow the rate of advance and double the anneal for each subsequent firing of the piece.  This is an investigation of the proposals.

Thickness determines ramp rates and annealing

Annealing soak lengths and cooling rates are related to thickness and complexity.  If no additions or complications are added between the previous and the current firing, there is no reason to extend the soak or decrease the rate of cooling.

You of course, need to consider what lay-up and process you are using in the additional firing.  Have you added any complexity to the piece in the previous or the current firing?  If so, you do need to consider how those changes will affect the firing requirements.

Fire polishing

The question to be asked is, “if the piece was properly annealed in the first firing and shows no significant stress, why do I need to change the firing?”

The answer is, “you only need to slow the heat up because it is a single piece now.”  You do need to know that the existing stress is minimal, of course. A note on stress testing is here.  If there is little or no stress from the previous firing, the annealing and cooling can be the same as the previous firing.  Nothing has changed. You are only softening the surface to a shine.  The anneal was adequate on the first firing, and it will be on the second.

If you are firing a pot or screen melt, you have added a complexity into the firing. This is because of the high temperatures used in the first firing.  It means you may wish to be more cautious about a re-firing to eliminate bubbles, or for a fire polish for the surface.

Frit layers

If you are adding confetti or thin layers of frit or powder you have not significantly changed the piece.  You can re-fire the piece as though you are fire polishing any other piece of the same dimensions.

Additional layers

If you are adding more full layers in subsequent firings, you need to reduce the rate of advance to top temperature.  You also need to extend the soak and reduce the cooling rate according to the new thickness of the piece.  This is because the piece is thicker, so the rate of advance needs to be slower, the time required to adequately anneal is longer, and the cooling rate needs to be slower.  All of these changes in scheduling are to accommodate the additional thickness.

Tack fusing additional pieces

If you are tack fusing pieces to the top of an already fired piece, you need to go slower than you would by just adding a full layer.  Tack fusing pieces to an existing piece adds a significant complication to the firing.  Tack fusing requires a firing for thickness between 1.5 and 2.5 times the actual total height of the piece.  The complexity added is the shading of the base glass from the heat radiating from the elements. 

For example, if your piece from the melt is 9mm/0.375", it would have been annealed with a 90 minutes soak. The first cool would be at 69C/127F per hour, and the second at 125C/225F per hour with the cool to room temperature at 415C/750F. If it shows no significant stress, you can fire polish and anneal in the same way as your initial firing.

But

If you tack fuse pieces on top, then you need to treat the piece as though it were between 15mm/0.625" (a little over 1.5 the thickness) and 25mm/1.0" (a little over 2.5 times) thick.  This would require a soak of 3 or 4 hours.  A cooling rate of between 40C/72F and 15C/27F per hour for the first cooling stage is needed. The second stage between will need a rate between 72C/130F and 27C/49F per hour. The final cooling to room temperature will be between 90C/162F and 240C/432F to room temperature.

Conclusion

If you have made no significant changes in thickness or complexity, the second firing can be the same annealing as the first firing. If you have altered the thickness or complexity of the piece, the second firing will need to be slower.

Further information is available in the ebook Low Temperature Kiln Forming.