Fig. 1 – Thermal Expansion Curves for several metals

In this article, I will explore the effect that thermal expansion has on joint clearance, and thus, on brazed joint strength and quality. It’s an important concept, and although it is well known in the brazing world, many folks today still do not take this topic seriously enough when designing brazed assemblies. This article is based on one I wrote many years ago for an in-house brazing publication at a brazing filler metal supplier. Included in this article I will look more closely at polymorphic metals, such as carbon steels, and will attempt to explain why they exhibit their very strange thermal expansion curves.

Please note that ALL metals expand (grow) when they are heated, and contract (shrink) when they are cooled. This fact has been thoroughly explored over the years, and data-tables have been published showing how fast each metal expands as temperature increases. This important information about the expansion characteristics of each metal should always be used in developing braze procedures when different kinds of base metals are to be brazed to each other. The success or failure of a braze procedure may very well depend on it!

Fig.1 shows typical thermal expansion data for some common base metals. It is obvious from these curves that different metals expand at different rates when heated. As an example, look at the two curves representing 302-stainless steel, and the curve representing tungsten carbide (WC). Notice from this chart that the stainless grows at a much faster rate, when heated, than does tungsten carbide. If these two metals were being brazed together, this difference in their expansion rates will be very important to take into consideration. Let’s look at this further.

Let’s assume that we were asked to braze a 302-stainless steel bar into a tungsten carbide ring, as shown in Fig. 2. As these two metals are heated up to brazing temperature, the brazing joint clearance between them will change as the stainless steel expands at a faster rate than the carbide. Thus the gap between them will get smaller (perhaps even close completely as they are heated).

Back to our example. Look at the assembly-diagram in Fig. 2.

Back to our example. Look at the assembly-diagram in Fig. 2.

Always remember that the optimal braze joint clearance that is needed for a successful braze occurs at brazing temperature since only at brazing temperature is the brazing filler metal (BFM) liquid and therefore able to flow through the joint by capillary action. Thus, it is critical that you use the metal expansion data from the charts to “back-calculate” from the needed clearance at brazing temperature down to the room temperature clearance needed to give you that desired clearance at brazing temperature when the two metals are heated (for most brazing we typically want a 0.000″-0.005″ {0.000-0.125mm} clearance between the faying surfaces of the joint at brazing temperature). For certain BFMs, it may need to be kept even tighter.

What if the I.D. of the thick-walled tungsten carbide ring exactly matched the O.D. of the round 302-stainless bar? What will happen as that assembly is heated to brazing temperature? The chart in Fig. 1 shows you that because the stainless expands faster than the tungsten carbide, the clearance (braze-gap) between the two parts will shrink (get tighter) as the temperature increases. In fact, the joint may become so tight that no BFM would be able to penetrate through it.

Similarly, if the stainless were the outer cylinder and the carbide was a smoothly fitting insert into the stainless, can you see that the gap clearance between the two surfaces would get wider with increasing temperature? The effect of thermal expansion must be taken into account ahead of time — before the parts are made, so that the metal parts may be appropriately machined before they are assembled for brazing in order to achieve optimal clearance at brazing temperature to let capillary energy do its work.

Brazing Challenge Question for Readers to Solve:

What room temperature radial clearance should be used for the carbide-stainless combination shown in Fig.2 if it were going to be brazed at 1950F (1065C) in a vacuum furnace, and a 0.0015″ (0.040 mm) radial clearance was desired at brazing temperature? The Answer to this problem can be found at the bottom of this article.

As we continue, I will now examine the thermal expansion curve for 1018 carbon steel to see why there are strange “reversals” in the thermal expansion curve for that alloy (and for similar metals). I will explore the effect that thermal expansion has on joint clearance, and thus, on brazed joint strength and quality of 1018 carbon-steel. For anyone doing high-temperature brazing of carbon-steel components using a high-temperature brazing filler metal (BFM) such as pure copper, it’s an important concept and needs to be understood.

As mentioned above, ALL metals expand when they are heated, and contract when they cooled. Fig.1 above once again shows typical thermal expansion data for some common base metals, indicating that different metals expand at different rates when heated. This month let’s look at the center curve, the one for 1018 carbon steel. Please note that it contains a strange “break” in the curve, and seems to show that the 1018 steel is actually shrinking while it is being heated. Is this true? Yes, this will actually happen.

In a laboratory setting, under very carefully controlled conditions, with very slow heating, this “hiccup” in the curve for 1018 steel actually takes place at one temperature, as shown in Fig. 2 below. But, in production brazing, where heating and cooling is much more rapid, this “hiccup” in the 1018-steel curve occurs over a temperature range from approximately 1200-1500 F (700-850C), as shown above in Fig. 1. Similar curves, i.e., expansion curves showing these “hiccups” during heating, will be seen for many different iron-bearing metals, including 4130 steel, and even 17-4PH, as examples.

Idealized thermal expansion curve for iron during very slow heating (source: see footnote 1)

Fig. 2 – Idealized thermal expansion curve for iron during very slow heating (source: see footnote 1)

To understand this unusual expansion/contraction phenomenon, we need to look at the actual arrangement of atoms within the metal. In general, metals tend to form very symmetrical, densely packed crystal structures. Two of the most common types of regularly repeating crystal lattice structures are known as “body-centered cubic” (BCC) and “face-centered cubic” (FCC), using nomenclature many of you may remember from the past.

Metals such as iron (and thus carbon steels) have a unique property called “polymorphism”, which, simply put, means that the metal can exist in alternate crystal forms, depending on the temperature and pressure being applied to it. The alpha-iron phase in 1018 steel is BCC at room temperature, but changes to gamma-iron (austenite), which has an FCC crystal structure, when heated to just above 1300F (710C), as shown in Fig. 3 below.

While changing from a BCC to an FCC crystal structure during heating, two things occur that cause shrinkage of the metal lattice structure: (1) heat is absorbed during the phase change, and (2) the packing of atoms becomes more efficient in FCC, allowing more iron atoms to fit in a given space than in the BCC alignment. Once the phase change has been completed, further heating will once again cause the steel to expand. The opposite reactions occur when the steel is cooled.

Change of iron's crystal structure during heating (source: see footnote 2)

Fig. 3 Change of iron’s crystal structure during heating (source: see footnote 2)

These seemingly insignificant “reversals” in thermal expansion and contraction curves for alloys such as 1018 steel can lead to major distortion problems (and even scrapped parts) if these changes are not taken into account during the furnace brazing cycle! For example, suppose you were brazing 1018 steel to an Inconel® 600 component. As you heat the assembly above approximately 1250F (675C), the 1018 steel would begin to shrink, as it started to realign its internal structure from BCC to FCC, while the Inconel would continue to expand almost linearly during that same time. As long as the parts were free to move relative to each other, you might not notice a problem. However, suppose the parts were tack-welded prior to brazing. When the assembly exceeds about 1250F (675C) and the Inconel continues to expand while the 1018 steel shrinks, either the tack-welds may break apart (losing part alignment), or the 1018 tubing may be forced to yield (stretch). This could then result in the tube buckling (distortion) at brazing temperature and also upon cooling.

To prevent this situation from becoming a problem when you are brazing assemblies that contain polymorphic materials, we recommend the following: (1) thermocouple the assemblies adequately so that you can accurately monitor the temperature of the different base metal components during heating, including that of the thinnest and thickest cross-sections; (2) include a built-in “hold” into your programmed furnace cycle at the beginning of the transition zones on both heating and cooling, in order to allow all parts “equalize”, i.e., to achieve thermal equilibrium, before proceeding further; and (3) move through the transition zones very slowly, monitoring your thermocouples for thermal equilibrium. This may add extra time to your furnace cycle, yet it can make the difference between producing good parts, or scrap!

Thank you for the proposed solutions sent in to us in response to the “Thermal-expansion Challenge” problem given to you above. Here’s the answer to the problem that readers were asked to solve!

The problem for readers to solve was this: What room temperature radial clearance should be used for the carbide-stainless combination shown in Fig.2 if it were going to be brazed at 1950F (1065C) in a vacuum furnace, and a 0.0015″ (0.040 mm) radial clearance was desired at brazing temperature?

Our answer: In order to reach an optimal radial gap clearance of about 0.0015″ (0.040 mm) at brazing temperature, our calculations show that you would need to start with a fairly “loose” radial clearance at room temperature of about 0.0135″/0.34mm (diametrical clearance of 0.027″/0.68mm) between the inner 302-stainless insert and the outer tungsten carbide sleeve-ring. How was this calculated? Explanation: Since we cannot assume that readers have access to other brazing resources to answer this, other than the thermal-expansion chart we included in the article, we wanted to see how folks would use the chart in the article to “solve” this problem. So, to determine the expansion of the stainless steel from room temperature up to brazing temperature, i.e., 70F to 1950F (about 20C to 1065C), it was necessary to extrapolate the thermal-expansion curve for 302-stainless up to 1950F/1065C (our original chart published in the article only went up to about 1800F/980C). See the “expanded” thermal-expansion chart, below. The extrapolation results in a predicted total expansion of about 0.021 inch per inch of thickness (or diameter). The carbide curve shows an expansion of only 0.009 inch per inch of thickness (or diameter) over this same temperature range. To make it easier to solve this problem, let’s start by letting the outside diameter (O.D.) of the stainless and the inside diameter (I.D.) of the carbide ring each have exactly a 1.0″ radius as a “starting position” for our calculations. Thus, the total expansion for the metal parts in this assembly when hearted up to 1950F can be read directly from their respective curves as 0.021″ and 0.009″. Thus, when heated from room temp up to 1950F (1065C), the 1.0″-dia stainless bar will grow 0.021″ in diameter, but the carbide-ring’s ID will only increase by 0.009″. Thus, the diameter of the stainless bar will grow more than the ID of the hole in the carbide ring, and the radial gap between them will actually get smaller as the temperature rises. Remember, the ID of the carbide ring does not get smaller when heated, but gets larger, just like the OD of the stainless bar. So this becomes only a differential expansion issue! The ID of the carbide ring does not shrink when heated, but gets larger, just like the outside diameter of the stainless bar.

Expanded Thermal-Expansion Chart

Expanded Thermal-Expansion Chart

The amount of the expansion of the outer member minus the amount of expansion of the inner member gives the net gap-clearance change. Thus, 0.009″-0.021″ = -0.12″ net diametrical gap “shrinkage” per inch of diameter (because the result of this calculation is a negative number), times “2” (because the stainless bar is actually 2-inches in diameter), for a total diametrical brazing-gap shrinkage of 0.024″! However, we do not want this amount of change (“shrinkage”) to close up the gap completely! When that “shrinkage” has happened, we still want there to be room for the brazing filler metal (BFM) to flow through the joint. That’s why we asked that the “final” resultant radial-clearance at brazing temperature still be 0.0015″ (0.003″ diametrical gap clearance). Thus, the starting gap clearance at room-temp needs to be 0.024″ + 0.003″ = 0.027″ diametrical — i.e., a 0.0135″-radial clearance (in order to provide a 0.0015″ radial-clearance at brazing temp). Congratulations to Travis Grohoske of Triumph Group in Ohio for coming closest with his estimate of 0.0067″-radial clearance at room temperature for this assembly! He probably was assuming a 1-inch diameter bar. Thus, for a 2-inch diameter stainless bar, he would have had an answer of 0.0134″ radial clearance needed. Wow!


  • Guy, Elements of Physical Metallurgy, 2nd ed. (MA, Addison-Wesley, 1959), p. 135, Fig. 5.6
  • Guy, Elements…, op.cit., p. 277, Fig. 7.17

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