In our last post we introduced the concept of anisotropy of 3D printed parts. For a summary - as we investigate at the stiffness of 3D printed parts in various directions, we see that it can vary widely depending on the slicing parameters used and the build orientation. Today, we want to perform some thought exercises on how layer height and extrusion width can influence stiffness and use numerical simulations to validate our thinking.

We’ll start by stating that layer height and extrusion width are not the only slicing parameters which influence the final stiffness of a 3D printed part, but for now we want to limit the scope of the discussion to introduce some basic concepts so we can expand our discussions in the future.

Let’s revisit the idea of 3D printing a cube using FFF, and assume we are using an unfilled plastic like PLA. As was discussed in our previous post, the final part is not a solid cube. In fact, it has local defects called voids which are located between filaments, as is shown in Figure 1. Figure 1.  Cross-section of an FFF part showing voids between printed filaments (1).

Now, there are a multitude of slicing parameters which can influence the size of voids, such as layer height, extrusion width, overlap, and even the extruder speed and temperature. We are just focusing on layer height and extrusion width in this discussion, which will allow us the ability to idealize the microstructure shown in Figure 1. If we assume the deposited filaments are ovals, we can compute the shape and size of the voids using some basic math as presented by Slice3r in this advanced flow path post (2) and shown in Figure 2.

Now that we can idealize the layer and void, we can use predictive methods like Finite Element Analysis (FEA) to predict the stiffness of the structure. We won’t get into the details of that here, but there are numerically efficient and accurate methods to predict the stiffness of a large, repeating structure (like Figure 1) by looking at a small, idealized portion of it (like Figure 2), and is also known as a Repeating Unit Cell (RVE).

Intuitively, we would say that there must be bounds on the stiffness of the “structure” in any given direction. We know that the structure cannot be stiffer than the material used in the filament, so the material stiffness must be the upper bound. Conversely, we also know that the presence of voids should reduce the stiffness, but the question is by how much?
Figure 3 shows the normalized stiffness of the filament and void “structure” (as-printed) plotted against the ratio of the extrusion width divided by the layer height. Normalized stiffness is the stiffness of the “structure” divided by the stiffness of the material used in the filament. Figure 3.  Normalized stiffness in the 3 principle directions for an FFF cube as a function of extrusion width divided by layer height. XX is along the filament direction, YY is transverse to the filament direction in the plane of the print bed, and ZZ is the through thickness direction parallel to the print direction.

We can come to a few interesting conclusions based on Figure 3:

1. The layered material is stiffest in the direction of the filament, and least stiff in the print direction. This makes sense due to the amount of void cross-sectional area affects each of these directions.

2. The stiffness is different in the ZZ direction when compared to the YY direction. This is not always intuitive, but is a consequence that the extrusion width must always be greater than the layer height – this is a physical manifestation of using a nozzle, which causes the voids to have a larger impact on stiffness reduction in the ZZ direction as the ratio of extrusion width top layer height becomes smaller.

3. As the ratio of extrusion width to layer height increases (flatter filament with less layer height), stiffness increases exponentially, and we can validate our intuition that the stiffness does indeed approach the stiffness of the filament material as the void volume is decreased.

4. After an extrusion width to layer height ratio of 6, returns on stiffness diminish significantly and likely will not be worth the increased print time.

What is not shown in the above plot is that the relationships are largely material independent, which indicates the effect the voids play in the overall stiffness of the as-printed part are much greater than one might realize at first blush.

We have just started investigating the effect of processing parameters on stiffness of an as-printed FFF structure. As we begin to complicate the problem by adding infill, this discussion can turn to optimizing slicing parameters in order to meet specific objectives such as stiffness and strength – something which will be saved for a later post.

# References

1. Rankouhi B, et al., Failure Analysis and Mechanical Characterization of 3D Printed ABS With Respect to Layer Thickness and Orientation, Journal of Failure Analysis and Prevention, Volume 13, Issue 3, pp 467-481, 2016.