Fused Deposition Modeling (FDM) Properties: A Micromechanics Perspective

Have you ever looked at the mechanical properties in an FDM material datasheet (one example shown below for Stratasys ULTEM-9085) and wondered why properties were prescribed in the non-traditional manner of XZ and ZX orientation? You may also have wondered, as I did, whatever happened to the XY orientation and why its values were not reported? The short (and unfortunate) answer is you may as well ignore the numbers in the datasheet. The longer answer follows in this blog post.

FDM_01

Mesostructure has a First Order Effect on FDM Properties

In the context of FDM, mesostructure is the term used to describe structural detail at the level of individual filaments. And as we show below, it is the most dominant effect in properties.

Consider this simple experiment we did a few months ago: we re-created the geometry used in the tensile test specimens reported in the datasheets and printed them on our Fortus 400mc 3D printer with ULTEM-9085. While we kept layer thickness identical throughout the experiment (0.010″), we modified the number of contours: from the default 1-contour to 10-contours, in 4 steps shown in the curves below. We used a 0.020″ value for both contour and raster widths. Each of these samples was tested mechanically on an INSTRON 8801 under tension at a displacement rate of 5mm/min.

As the figure below shows, the identical geometry had significantly different load-displacement response – as the number of contours grew, the sample grew stiffer. The calculated modulii were in the range of 180-240 kpsi. These values are lower than those reported in datasheets, but closer to published values in work done by Bagsik et al (211-303 kpsi); datasheets do not specify the meso-structure used to construct the part (number of contours, contour and raster widths etc.). Further, it is possible to modify process parameters to optimize for a certain outcome: for example, as suggested by the graph below, an all-contour design is likely to have the highest stiffness when loaded in tension.

FDM-02

Can we Borrow Ideas from Micromechanics Theory?

The above result is not surprising – the more interesting question is, could we have predicted it? While this is not a composite material, I wondered if I could, in my model, separate the contours that run along the boundary from the raster, and identify each as it’s own “material” with unique properties (Er and Ec). Doing this allows us to apply the Rule of Mixtures and derive an effective property. For the figure below, the effective modulus Eeff becomes:

Eeff = f.Ec + (1-f).Er

where  represents the cross-sectional area fraction of the contours.

FDM-3

With four data points in the curve above, I was able to use two of those data points to solve the above equation simultaneously and derive Er and Ec as follows:

Er = 182596 psi
Ec = 305776 psi

Now the question became: how predictive are these values of experimentally observed stiffness for other combinations of raster and contours? In a preliminary evaluation for two other cases, the results look promising.

FDM-4

So What About the Orientation in Datasheets?

Below is a typical image showing the different orientations data are typically attributed to. From our micromechanics argument above, the orientation is not the correct way to look at this data. The more pertinent question is: what is the mesostructure of the load-bearing cross-section? And the answer to the question I posed at the start, as to why the XY values are not typically reported, is apparent if you look at the image below closely and imagine the XZ and XY samples being tested under tension. You will see that from the perspective of the load-bearing cross-section, XY and XZ effectively have the similar (not the same) mesostructure at the load-bearing cross-sectional area, but with a different distribution of contours and rasters – these are NOT different orientations in the conventional X-Y-Z sense that we as users of 3D printers are familiar with.

fdm-5

Conclusion

The point of this preliminary work is not to propose a new way to model FDM structures using the Rule of Mixtures, but to emphasize the significance of the role of the mesostructure on mechanical properties. FDM mesostructure determines properties, and is not just an annoying second order effect. While property numbers from datasheets may serve as useful insights for qualitative, comparative purposes, the numbers are not extendable beyond the specific process conditions and geometry used in the testing. As such, any attempts to model FDM structure that do not account for the mesostructure are not valid, and unlikely to be accurate. To be fair to the creators of FDM datasheets, it is worth noting that the disclaimers at the bottom of these datasheets typically do inform the user that these numbers “should not be used for design specifications or quality control purposes.”

If you would like to learn more and discuss this, and other ideas in the modeling of FDM, tune in to my webinar on June 28, 2016 at 11am Eastern using the link here, or read more of my posts on this subject below. If you are reading this post after that date, drop us a line at info@padtinc.com and cite this post, or connect with me directly on LinkedIn.

Thanks for reading!

~

Two related posts:

Constitutive Modeling of 3D Printed FDM Parts: Part 2 (Approaches)

In part 1 of this two-part post, I reviewed the challenges in the constitutive modeling of 3D printed parts using the Fused Deposition Modeling (FDM) process. In this second part, I discuss some of the approaches that may be used to enable analyses of FDM parts even in presence of these challenges. I present them below in increasing order of the detail captured by the model.

  • Conservative Value: The simplest method is to represent the material with an isotropic material model using the most conservative value of the 3 directions specified in the material datasheet, such as the one from Stratasys shown below for ULTEM-9085 showing the lower of the two modulii selected. The conservative value can be selected based on the desired risk assessment (e.g. lower modulus if maximum deflection is the key concern). This simplification brings with it a few problems:
    • The material property reported is only good for the specific build parameters, stacking and layer thickness used in the creation of the samples used to collect the data
    • This gives no insight into build orientation or processing conditions that can be improved and as such has limited value to an anlayst seeking to use simulation to improve part design and performance
    • Finally, in terms of failure prediction, the conservative value approach disregards inter-layer effects and defects described in the previous blog post and is not recommended to be used for this reason
ULTEM-9085 datasheet from Stratasys - selecting the conservative value is the easiest way to enable preliminary analysis
ULTEM-9085 datasheet from Stratasys – selecting the conservative value is the easiest way to enable preliminary analysis
  • Orthotropic Properties: A significant improvement from an isotropic assumption is to develop a constitutive model with orthotropic properties, which has properties defined in all three directions. Solid mechanicians will recognize the equation below as the compliance matrix representation of the Hooke’s Law for an orthortropic material, with the strain matrix on the left equal to the compliance matrix by the stress matrix on the right. The large compliance matrix in the middle is composed of three elastic modulii (E), Poisson’s ratios (v) and shear modulii (G) that need to be determined experimentally.
Hooke's Law for Orthotropic Materials (Compliance Form)
Hooke’s Law for Orthotropic Materials (Compliance Form)

Good agreement between numerical and experimental results can be achieved using orthotropic properties when the structures being modeled are simple rectangular structures with uniaxial loading states. In addition to require extensive testing to collect this data set (as shown in this 2007 Master’s thesis), this approach does have a few limitations. Like the isotropic assumption, it is only valid for the specific set of build parameters that were used to manufacture the test samples from which the data was initially obtained. Additionally, since the model has no explicit sense of layers and inter-layer effects, it is unlikely to perform well at stresses leading up to failure, especially for complex loading conditions.  This was shown in a 2010 paper that demonstrated these limitations  in the analysis of a bracket that itself was built in three different orientations. The authors concluded however that there was good agreement at low loads and deflections for all build directions, and that the margin of error as load increased varied across the three build orientations.

An FDM bracket modeled with Orthotropic properties compared to experimentally observed results
An FDM bracket modeled with Orthotropic properties compared to experimentally observed results
  • Laminar Composite Theory: The FDM process results in structures that are very similar to laminar composites, with a stack of plies consisting of individual fibers/filaments laid down next to each other. The only difference is the absence of a matrix binder – in the FDM process, the filaments fuse with neighboring filaments to form a meso-structure. As shown in this 2014 project report, a laminar approach allows one to model different ply raster angles that are not possible with the orthotropic approach. This is exciting because it could expand insight into optimizing raster angles for optimum performance of a part, and in theory reduce the experimental datasets needed to develop models. At this time however, there is very limited data validating predicted values against experiments. ANSYS and other software that have been designed for composite modeling (see image below from ANSYS Composite PrepPost) can be used as starting points to explore this space.
Schematic of a laminate build-up as analyzed in ANSYS Composite PrepPost
Schematic of a laminate build-up as analyzed in ANSYS Composite PrepPost
  • Hybrid Tool-path Composite Representation: One of the limitations of the above approach is that it does not model any of the details within the layer. As we saw in part 1 of this post, each layer is composed of tool-paths that leave behind voids and curvature errors that could be significant in simulation, particularly in failure modeling. Perhaps the most promising approach to modeling FDM parts is to explicitly link tool-path information in the build software to the analysis software. Coupling this with existing composite simulation is another potential idea that would help reduce computational expense. This is an idea I have captured below in the schematic that shows one possible way this could be done, using ANSYS Composite PrepPost as an example platform.
Potential approach to blending toolpath information with composite analysis software
Potential approach to blending toolpath information with composite analysis software

Discussion: At the present moment, the orthotropic approach is perhaps the most appropriate method for modeling parts since it is allows some level of build orientation optimization, as well as for meaningful design comparisons and comparison to bulk properties one may expect from alternative technologies such as injection molding. However, as the application of FDM in end-use parts increases, the demands on simulation are also likely to increase, one of which will involve representing these materials more accurately than continuum solids.

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.

Multiscale structure of an FDM part
Multiscale structure of an FDM part

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.
Stratasys ULTEM 9085 datasheet material properties showing anisotropy
Stratasys ULTEM 9085 datasheet material properties showing anisotropy
  • 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.
Ultimate Tensile Strength of FDM ULTEM 9085 for three different build orientations, compared to injection molded value (84 MPa) for two different data sources, and two different process parameter settings from the same source. On the right are shown the different orientations and process parameters varied.
Ultimate Tensile Strength of FDM ULTEM 9085 for three different build orientations, compared to injection molded value (84 MPa) for two different data sources, and two different process parameter settings from the same source. On the right are shown the different orientations and process parameters varied.
  • 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.
FDM Defects: Staircase error (top), Internal defects (bottom)
FDM Defects: Staircase error (top), Internal defects (bottom)

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