Why 3D Prints Warp

Many people blame FFF 3D print warping on uneven cooling, or assume it’s an inherent property of certain plastics. These explanations are close, but miss the mark.

Why do 3D prints warp?

The cause of FFF warping is pretty straightforward. As newly deposited strands of plastic cool, they solidify and shrink. But the previous layer has already had a chance to cool, and thus has already contracted. If you adhere a hot layer onto a cold layer, the two layers are thermally expanded by different amounts, so when they reach thermal equilibrium the new layer will contract relative to the lower layer. This creates a residual thermal stress in the plastic strands. The bottom of the upper strand is under tension, and the top of the lower strand is under compression. Put another way, there’s a shear stress at the interface between the strands. If these stresses exceed the part’s mechanical stiffness and build plate adhesion, warping will occur. It’s kind of like the effect used in bimetallic strips in thermostats and the like.

What happens with poor build plate adhesion:

FFF thermal contraction warping

What happens with adequate build plate adhesion:

Thermal stresses without warping

As the graphic shows, thermal contraction causes warping if the part is not sufficiently constrained from shrinking. If the part is constrained by build plate adhesion, then cooling will create thermal stresses (locked-in forces) instead of thermal strain (warping).

There are three possible outcomes from this differential layer contraction phenomenon:

  1. If thermal stresses exceed the strength of the build plate adhesion, edge curling will occur.
  2. If thermal stresses exceed the internal layer adhesion of the part, cracking will occur.
  3. If neither curling nor cracking occur, the layer interface will likely retain residual internal stresses that weaken the printed part against layer delamination under load.

Most casual printer users assume that if they can successfully prevent edge curling and cracking then the print is good to go. But that’s false: high residual warping stresses will permanently weaken the printed part. The interlayer bond is pre-stressed and will consequently fail with lower applied stress. The fight against warping stresses shouldn’t stop just because you get your corners to stick.

The Root Cause

The best way to address warping stresses is to understand and minimize the underlying drivers for thermal stress in printing conditions.

First, it is important to understand that molten plastic flows (duh) and fluid flow allows internal stresses to relax very rapidly (until the plastic cools more or less solid). The transition between “viscoelastic fluid” and “very soft solid” occurs at the glass transition temperature Tg or “glass point” of the polymer. Loosely speaking, this is the temperature where the long-chain polymer molecules no longer have enough thermal kinetic energy to slide freely past each other. The polymer kind of just “locks up.” It’s not a sharp transition like a melting point — more of an inflection point in the measured properties-vs-temp curve of the plastic.

Thermal contraction doesn’t generate internal stress if the material can flow. So, only cooling below the glass point matters to thermal contraction for warping. If the filament’s glass point is 55C like PLA and the print environment is 30C, that is 25C of subcooling. We don’t care that the PLA had to cool from, say, 210C to 55C before it dropped to Tg and really solidified. That cooling doesn’t count here.

The degrees of subcooling can be multiplied by the coefficient of thermal expansion for the plastic to find the expected total proportion of shrinkage for the extruded strand. This isn’t necessarily an exact number, because polymers don’t have entirely linear thermal expansion/contraction, but it’s a good estimate.

Thermal expansion measurement for Stratasys ABS ESD7 shows thermal contraction only starts around 80C for that particular blend, and is fairly linear after that:

Thermal expansion measurement of Stratasys ABS ESD7

Image Source

If the thermal contraction is constrained — as we need it to be to avoid warping — the plastic must become stressed instead of shrinking. This is the same elastic stress as you would get if you allowed the plastic to shrink as it cooled, then pulled on it to stretch it back out to its original dimension. The stiffness or ratio of force to stretch (stress/strain) for a material is called the the Young’s modulus. We can combine these parameters to estimate how much warping stress to expect from a given printing situation.

The magnitude of thermal stress in a constrained 3D print is roughly proportional to the coefficient of thermal expansion of the plastic, the amount of cooling below the glass point, and the young’s modulus of the material. Here’s the equation:

thermal stress ~= Young’s Modulus * coefficient of thermal expansion * deltaT

This formula drives three key conclusions:

  1. Stiff plastics warp more than rubbery plastics.
  2. Plastics with a large coefficient of thermal expansion warp more than those with a low coefficient of thermal expansion.
  3. Plastics with high glass points will warp more than those with low glass points unless the build chamber is heated to an appropriate temperature.

Here are some examples of how this affects your filament selection:

  • ABS warps a lot in typical printers and is prone to layer delamination because it has a relatively high glass point of 105C. But a heated build chamber of ~85C makes it a dramatically better printing material.
  • PLA’s glass point is only 55C, so it experiences little subcooling at room temp and thus doesn’t warp much. However, it’s quite stiff, so it will warp atrociously in a cold garage.
  • Rubbery TPUs are very low-warp because they can accommodate very large contraction strains with low stress.
  • Composites with carbon fiber or fiberglass experience low shrinkage due to the low coefficient of thermal expansion of the reinforcing material, and thus warp much less than the equivalent unfilled plastic.

There’s another big factor to add to the coefficient of thermal expansion. The polymer’s level of crystallinity is also extremely important to the warping behavior. A crystalline arrangement of polymer molecules is orderly and takes up less volume than a jumbled-up or amorphous arrangement of the same molecules. Crystalline polymers experience rapid shrinkage when they cool through a temperature where they transition from a disorganized semi-solid state to an organized crystalline solid state.

Crystalline polymers like PP, UHMWPE, and POM experience high shrinkage as they crystallize, and thus warp so much that very few people print with them. In comparison, amorphous polymers like ABS or PETG do not warp anywhere near as much as crystalline polymers with the same glass point and stiffness. (Yes, ABS could be much worse!)

PLA has a very complex semi-crystalline behavior which depends on the filament blend and additives. It can pass through multiple different crystalline phases with different molecular arrangements as it cools, ages, or is annealed. But for practical purposes, the glass point is so low that we don’t need to worry too much about its crystalline behavior from a warping standpoint. 

Nylon has some interesting crystalline properties that will probably be the subject of a future post. The short version is that it warps different amounts depending on print settings like layer height and nozzle speed.

How to Solve It

Filament selection is obviously the first step in managing warping stresses. A filament on its own isn’t inherently “low-warp” or “high-warp,” but its properties do interact with the print environment in predictable ways to drive warping.

Elastic/rubbery plastics with low glass points experience the least warping in typical desktop printers. PETG, TPUs, and “tough” PLA are good examples.

Stiff plastics with high glass points and crystalline plastics both experience high warping unless properly managed. ABS, polycarbonate, and PEEK require appropriately high ambient temperatures to print well. Polypropylene requires compositing with a low-shrinkage fiber to print well.

Professional FFF 3d printers use heated build chambers. This is the best possible solution for high-Tg plastics. By maintaining a chamber temp below-but-near the glass point of the plastic, the amount of thermal contraction is minimized, and there is very little tendency to warp. Each filament has a specific optimal chamber temperature in its “creep zone” where it not only has minimal thermal contraction, but can also slowly relax any significant internal stresses… resulting in minimum warp and maximum part strength. This is often around 20C below the glass point. For example, ABS prints extremely well in an 85C chamber, and PLA prints extremely well in a 35C chamber (with adequate airflow for print cooling).

Filament selection is sometimes fixed by print material property requirements, and heated build chambers have historically been challenging for desktop printers due to a combination of patents, cost, and engineering complexity. So the two primary methods to prevent warping in desktop printers are heated build plates and adhesion surfaces:

  • Adhesion surfaces work by mechanically holding the print in a non-warped position until the print is completed. This means the internal stresses from thermal contraction are resisted by reaction stresses in the (much stiffer) build plate. However, this does nothing for delamination cracking and residual stress.
  • Heated build plates utilize a combination of effects. They increase print adhesion with many print surfaces that utilize diffusion bonds, such as kapton or PEI. They also reduce subcooling of the bottom 5-10 mm of the print near the build plate, and thus decrease thermal contraction in the critical “foundation” of the print. At finely-tuned temperatures, they also maintain some of the plastic near its glass point in the “creep range,” thus allowing stresses to slowly relax.

The optimal heated build plate temperature tends to run a little higher than the optimal heated chamber temperature, for two distinct reasons:

  1. Build plate temperature is typically measured from the bottom or middle of the stack, near the heater, not the actual print surface.
  2. The print layers cool closer to ambient air temperature as the print gets taller, so only the first few layers actually experience the full bed surface temperature.

However, excessive build plate temperatures (at or over the glass point) actually exacerbate warping, because the bottom of the print is too soft to resist the warping stresses generated by higher, cooler layers as the print gets taller. Plastic has no meaningful strength at its glass point. It’s barely solid.

Ultimate tensile strength of Stratasys M30 ABS drops rapidly to zero between 80C and 105C:

Tensile strength of ABS vs temperature

Image Source

A good rule of thumb for build plate measured surface temperature is 10C below the glass point of the filament. (The commanded temperature may need to be higher due to sensor placement as noted above.) However, it may be more advantageous to run a higher temperature closer to the glass point for the first few layers for maximum adhesion and minimum internal stress, and then reduce the build plate temperature to a cooler setting that fully solidifies the plastic. This lays down a low-stress foundation at the start of the print, and then cools it solid as the print rises so the cooler upper layers cannot deform the foundation.

A heated build plate with an adhesion surface appropriate for the the filament will resolve most warping issues — at least as far as eliminating corner curling and producing geometrically-accurate prints. It will also provide quite a bit of heat to an enclosed printer to warm the ambient air and reduce subcooling. However, for maximum print strength with ABS, or to print very high Tg plastics like PC and PEEK, the proper solution is really a heated build chamber. That’s the only way to fully control the thermal contraction of the entire print.

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