It’s been a while since I published my last post – I wrote it at the conclusion of my project and then life happened – graduation, full time job, tons of traveling, moving, and fun and exciting new hobbies. Since then, Markforged has released many new printers and materials to further improve their fiber reinforcement system. Anyways, here are the full results of the project:
I hinted at some of the statistics I was planning on doing in my last post, when I ran a t-test on the two different sets of samples that came off of the Markforged 3D printer. My main goal with all of the tests I’ve been running has primarily been to get a sense for anisotropy on the different printers I was working with based on tensile test data. I.e., I wanted see how the strength of 3D printed components compare across the X, Y, and Z axes. I’ve run tensile tests on specimens coming off of the MakerBot Replicator 2, the MakerBot Replicator 2X, the Stratasys Dimension 1200es, and the Mark One, with both pure nylon and with embedded Kevlar. As you read from my preliminary results, it seemed like the Y axis was a little bit more brittle than the X axis on some of the printers I tested, and overall the Z axis was weaker and more brittle. It also seemed like printers with slicers that would slice individual parts before laying them out on the build plate created specimens with more consistent data than printers that would slice all of the parts after they were all laid out. This is because the infill pattern for a part sliced before build plate placement remains the same wherever it is, whereas infill pattern varies depending on location on the build plate if all the parts are sliced after layout. You can read more about this in my post covering my initial findings.
In general, the goal of this project was to get a sense for the anisotropy in material properties on a few different printers. I’ve collected more data and compiled all of it so that I could run some statistical analysis on my parts. Recently I posted about how the quality of the nylon filament on the Mark One can dramatically affect the material properties of the parts it produces, and why it is important to keep your nylon in a well-sealed container. I’ve now gone through all of the data from all the other printers as well, and I will be running one-way ANOVA (analysis of variance) tests across sample sets to determine whether there are any significant differences that would suggest anisotropy in the material properties of each printer. For some clarification, I consider the X axis of a printer to be the side parallel to the front of the printer on the plane of the build plate, the Y axis to be perpendicular to that but also on the same plane, and the Z axis normal to the build plate, as shown in the diagram below.
The ANOVA test compares the means and standard deviations of each set of specimens to determine the probability that the data from each of the three axes can be considered to be from the same group of samples. If that probability is very low (the standard is p<0.05, or 5%, which is what I will be using), I can use what is called a post hoc test to inform which axes are different than the others: the ANOVA only tells me if there is a difference or not. In this experiment, I used the Fischer’s Least Significant Difference method for my multiple comparisons. This is one of the less conservative procedures, but I chose to use it because it may expose more differences rather than fewer, and the possibility that there could be a difference is more important to show than none in this experiment. In the table below I show the probabilities if isotropy (that the properties along the X, Y, and Z axes come from the same group) for each material property I studied on each printer as determined by the ANOVA tests. In each section below, I explain the results I obtained from the post hoc tests and identify the axes and material properties that are different.
From a brief look at the raw outputs of the data as shown above, it looks like the most mechanical property differences between the axis directions lie in the strain at fracture and the toughness. The strain at fracture and toughness are linked: toughness (how much energy a part absorbs before failure) corresponds to the area under the stress-strain curve, while strain at fracture (the strain at which the specimen breaks) is basically the “width” of the bounding region of the curve. From the post hoc test results I share below, it is clear that these two properties are statistically different in specimens printed in the Z direction. More specifically, parts printed along this axis tend to be much weaker than when printed along the X and Y axes. Parts printed along the X and Y axes tend to have more similar mechanical properties.
Stratasys Dimension 1200es
As shown from the ANOVA test results, every property for parts printed on the Stratasys Dimension 1200es printer apart from yield strength was statistically dissimilar across axes. But even so, the yield strength was just over the 5% mark at 0.0535, so it was pretty close. As an example to show how the post hoc multiple comparison test works, I’ll show what it returns. The ANOVA test takes as inputs the values for the material property in question, sorted by whichever axis the sample was printed on. In this case, I’ll be looking at the modulus, so my inputs comprised of a matrix of 3 columns, with each column representing an axis of the printer. The ANOVA test returns some statistical data about the three sets of samples and the probability it determined for the samples being in the same group. Here’s a box and whisker plot of the three sets of samples (X, Y, and Z):
This shows the median (the centerline), the 25th and 75th percentiles (the bottom and top of the box), the standard deviation intervals (the notch endpoints) and the data extremes (the limits of the whiskers).
The multiple comparison test takes all this data and compares data from each axis to data from each other axis in sets of two, so it looks at the similarities between properties along the X and Y axes, X and Z axes, and Y and Z axes. We only need to run the multiple comparison test if the ANOVA returned a probability less than 5%. From just the ANOVA, we can see if all the data from each axis is statistically similar or not. The post hoc test then uses this information from the ANOVA to determine one of two things: the material property in question is statistically different across all 3 axes, or one axis has statistically different properties than the other two. The test then returns something like this:
This plot shows that Group 3, the modulus of the Z axis on this printer, is statistically different than the other two, while the modulus along X and Y axes are the same. We can then do this for each of the four properties studied, and for each printer, to determine where differences lie.
So, on the Stratasys Dimension 1200es printer, the modulus was higher and significantly different in the Z axis than on the other two. The yield strength was statistically similar across axes, but only by a small margin. Notice on the stress-strain plot, one outlier on the Z axis had a higher yield strength than the others, which likely brought the mean up enough to affect the comparison. Had this not happened, the yield strength would have probably been different along the Z axis like the modulus. In strain at fracture and toughness, parts printed along the X and Y axes were again similar, and those along the Z axis were weaker in both properties.
One interesting feature of the Stratasys printer is its consistency. From looking at the stress-strain curve, you may not think the modulus (the slope of the linear region) is that different across the three axes. However, because the printer is so consistent in its results (all modulus values on this printer had a standard deviation of less than 10%), the difference stands out. The average modulus along the Z axis is only about 15% greater than along X and Y, but the values are still statistically discernable. In practice, this probably won’t make a huge difference, but it is important to note.
The strain at fracture and toughness were statistically different because the brittle nature of parts printed along the Z axis: the strain at fracture in specimens along the X and Y axes were nearly 100% greater than in the Z axis. This is because when parts are loaded along the X and Y axes, the “strands” of filament are being pulled upon, so their strength is coming from the material properties of the original filament. The Z axis strength comes from “seams” formed between layers of strands laid down on top of one another, which makes it weaker because the material’s adhesion to itself is not as strong as the material alone.
MakerBot Replicator 2
There is a lot more variability in the material properties from parts on the Replicator 2 than from the Stratasys printer. The yield strength, strain at fracture, and toughness all have very low probability values, and the probability that the modulus is isotropic is very near 5%. The variability is borne out by the statistics – many of the properties on different axes have standard deviations exceeding 10%, and along the Z axis properties exceed 30% standard deviation. The multiple comparison tests returned that in yield strength and toughness, parts printed along the Z axis are different than those along the X and Y axes, while the X and Y axes remain statistically similar. However, in strain at fracture, the property on each axis returned as statistically different, as shown in the plot below.
It is unusual that there is this difference in strain at fracture and not in toughness. Mathematically, the slight differences in yield strength and modulus drown out differences in toughness because they affect the area under the curve and end up making it relatively similar to the X axis. Physically, I hypothesize this is because of the way the build plate is constrained. Overall, it is less secure than the build plate on the Stratasys because it is held on by small clips, requires manual leveling, and overall is less flat. More specifically, the Y axis of the build plate is better constrained than the X axis because the build plate is secured by three clips on either long edge of the plate. These clips are connected to a frame via three bolts near the center of the plate, which are attached to a frame that connects to the Z axis lead screw of the printer. This leaves the sides of the plate to flex and wobble, and could affect the consistency to which the material is laid down: there is more wobble in the X axis thus the filament could act differently for a number of reasons: it sticking to the build plate differently, it not quite being laid down consistently, it not cooling quite right as a result etc. This then changes the material behavior enough to make a difference: Because the Y axis is more constrained, it is more brittle, while the X axis can stretch more because it wasn’t laid down and cooled as consistently.
One of the other big take homes here is that the Z axis is just terrible. The average material property values on specimens are consistently less than half those of the other axes, and its consistency is atrocious, with standard deviations exceeding 30%. So if you think parts loaded in the Z direction will be strong, think again, because it is clearly not reliable.
MakerBot Replicator 2X
The Replicator 2X behaved relatively similarly to the Replicator 2 in its anisotropy. The moduli of specimen on this printer were statistically similar, with a probability of 71% that they were from the same group. For the other three properties, the properties of parts printed along the Z axis differed from those along the other two axes, while parts along the X and Y axes had statistically similar properties, as we’ve seen occur previously.
The yield strength, strain at fracture, and toughness along the Z axis were all pretty variable – the toughness had a standard deviation of 67%. This is because of the behavior in tension when parts are pulled along their Z axis. As I explained earlier, because of the seams between layers, the yield strength is based upon the two layers that have the weakest seam. This limiting factor is the part’s weakest link, making the yield strength extremely unpredictable and also affecting the strain at fracture and the toughness as a result, because the Z axis has a mostly linear behavior. The build plate on a MakerBot Replicator 2X is a bit better constrained than on the Replicator 2 – it cannot actually be removed, it is fixed to the Z axis instead of being removable, so there is not as much of a difference between the X and Y axes.
While the strain at fracture and toughness on the Markforged 3D printer with pure nylon were different in specimens printed on the Z axis than in those printed on the X and Y axes, surprisingly, the ANOVA and post hoc test returned that the modulus and yield strength across specimens on all three axes were statistically similar.
It’s clear that the strain at fracture and toughness are different because parts printed along the Z axis do not stretch nearly as much as those along the X and Y axes. But why are the yield strength and modulus similar on specimens printed regardless of the axis they were printed along? As I explained in my previous post, there is a huge source of variation depending on the age of the nylon filament. Even within that, it’s pretty variable. The range of the yield strength and moduli of parts printed on the Z axis are large enough to encompass the data from the other two axes, so although on the surface these can be considered “statistically similar,” take this with a grain of salt. You really won’t know how weak or strong the Z axis will be, because it is not nearly as reliable as the other two axes. With standard deviations ranging from 20% to 130%, its material properties are so variable that it drowned out any statistical differences so we can’t actually tell whether or not they are from the same group. So the bottom line is don’t trust the Z axis because you won’t know what to expect.
One of the cool things about the Mark One is its ability to print in high strength materials like fiberglass, carbon fiber, and Kevlar. I printed some Kevlar samples to see how they would affect the material properties. Because the Mark One only has the capability to lie down Kevlar fiber in on the XY plane, I only ran tests on those axes and thus only had two data sets to compare instead of the usual 3, so I ran a t-test on the data sets instead of an ANOVA. The t-test returned that all of the materials on the X and Y axes were statistically similar.
This is probably because the Kevlar reinforcement makes the inconsistencies in the nylon nearly negligible. The Kevlar strands itself are very consistent, and this makes the specimen act like composite materials. As the Kevlar is the more brittle, but stronger material, the printed piece behaves more like the Kevlar. Once the Kevlar strands snap after a given extension, only nylon holds the part together because nylon has a higher strain at fracture, thus the material starts to behave like nylon. Reinforcing nylon with Kevlar on the Mark One made its material properties much more consistent. If you care about mechanical properties, I suggest only use it with the Kevlar because of consistency.
The biggest differences in each of the printers I tested were in how the properties of parts printed along the Z axis compared to those on the X and Y axes. For every printer, the parts printed in the Z axis direction differed in strain at fracture and toughness, which was to be expected because the Z axis is much more brittle than the other two: specimens are being pulled apart at their seams instead of along strands of filament. This also causes a variability problem, because the weakest link in the part along the Z axis is not a matter of the strength of the material itself, but rather how well each layer is adhered to the next. For any reason, if one layer is not as well adhered as the other, that layer defines the maximum Z strength of the part. On most printers, the seams don’t stick together quite the same way every time, so it comes down to fracture mechanics. The part ends up having a sort of crack-propagation behavior, in which the weakest “crack” splits first.
While on the desktop 3D printers – the two MakerBots and the Markforged printer – this caused a huge issue because all of the properties were highly variable; on the Stratasys printer the properties still remained relatively consistent. Because the enclosure of the printer is heated, the seams end up melding together and sticking reliably to each other, achieving better and more consistent results. However, the strain at fracture was still lower than parts printed on the other axes, so the adhesion still isn’t as good as along the other axes.
Another interesting feature of parts printed along the Z axis was that before they broke, they had moduli comparable to those of parts printed on the other two axes. This suggests that before failure, the seams do not affect the modulus of the specimen as the modulus is coming more from the material itself, within the layers and strands, not between them, so the moduli could even be considered isotropic.
So in general, what I really took from this is that strength along the Z axis is highly variable because of its failure behavior, and along other axes properties are usually comparable. Additionally, on less robust printers, the properties of a part – even when laid out on the print bed plane, can vary depending on the direction. The cool part of this experiment was testing the Mark One, because I could really see what the fiber reinforcement did to the properties of the nylon as a composite material. It makes it a lot more reliable and consistent, which is really cool! Since the Mark One, Markforged has released many new materials and products that have drastically improved their system reliability and performance.