Constitutive Modeling of 3D Printed FDM Parts: Part 1 (Challenges)

As I showed in a prior blog post, Fused Deposition Modeling (FDM) is increasingly being used to make functional plastic parts in the aerospace industry. All functional parts have an expected performance that they must sustain during their lifetime. Ensuring this performance is attained is crucial for aerospace components, but important in all applications. Finite Element Analysis (FEA) is an important predictor of part performance in a wide range of indusrties, but this is not straightforward for the simulation of FDM parts due to difficulties in accurately representing the material behavior in a constitutive model. In part 1 of this article, I list some of the challenges in the development of constitutive models for FDM parts. In part 2, I will discuss possible approaches to addressing these challenges while developing constitutive models that offer some value to the analyst.

It helps to first take a look at the fundamental multi-scale structure of an FDM part. A 2002 paper by Li et. al. details the multi-scale structure of an FDM part as it is built up from individually deposited filaments all the way to a three-dimensional part as shown in the image below.

This multi-scale structure, and the deposition process inherent to FDM, make for 4 challenges that need to be accounted for in any constitutive modeling effort.

• Anisotropy: The first challenge is clear from the above image – FDM parts have different structure depending on which direction you look at the part from. Their layered structure is more akin to composites than traditional plastics from injection molding. For ULTEM-9085, which is one of the high temperature polymers available from Stratasys, the datasheets clearly show a difference in properties depending on the orientation the part was built in, as seen in the table below with some select mechanical properties.

• Toolpath Definition: In addition to the variation in material properties that arise from the layered approach in the FDM process, there is significant variation possible within a layer in terms of how toolpaths are defined: this is essentially the layout of how the filament is deposited. Specifically, there are at least 4 parameters in a layer as shown in the image below (filament width, raster to raster air gap, perimeter to raster air gap and the raster angle). I compiled data from two sources (Stratasys’ data sheet and a 2011 paper by Bagsik et al that show how for ULTEM 9085, the Ultimate Tensile Strength varies as a function of not just build orientation, but also as a function of the parameter settings – the yellow bars show the best condition the authors were able to achieve against the orange and gray bars that represent the default settings in the tool.  The blue bar represents the value reported for injection molded ULTEM 9085.

• Layer Thickness: Most FDM tools offer a range of layer thicknesses, typical values ranging from 0.005″ to 0.013″. It is well known that thicker layers have greater strength than thinner ones. Thinner layers are generally used when finer feature detail or smoother surfaces are prioritized over out-of-plane strength of the part. In fact, Stratasys’s values above are specified for the default 0.010″ thickness layer only.
• Defects: Like all manufacturing processes, improper material and machine performance and setup and other conditions may lead to process defects, but those are not ones that constitutive models typically account for. Additionally and somewhat unique to 3D printing technologies, interactions of build sheet and support structures can also influence properties, though there is little understanding of how significant these are. There are additional defects that arise from purely geometric limitations of the FDM process, and may influence properties of parts, particularly relating to crack initiation and propagation. These were classified by Huang in a 2014 Ph.D. thesis as surface and internal defects.
  • Surface defects include the staircase error shown below, but can also come from curve-approximation errors in the originating STL file.
  • Internal defects include voids just inside the perimeter (at the contour-raster intersection) as well as within rasters. Voids around the perimeter occur either due to normal raster curvature or are attributable to raster discontinuities.

Thus, any constitutive model for FDM that is to accurately predict a part’s response needs to account for its anisotropy, be informed by the specifics of the process parameters that were involved in creating the part and ensure that geometric non-idealities are comprehended or shown to be insignificant. In my next blog post, I will describe a few ways these challenges can be addressed, along with the pros and cons of each approach.

Click here to see part 2 of this post