Structural stability of thin overhanging walls during material extrusion additive manufacturing of thermoset-based ink

https://doi.org/10.1016/j.addma.2022.102677Get rights and content

Highlights

  • An uncured epoxy ink for DIW is approximated as an elastic-plastic solid.

  • Basic beam mechanics analyses accurately predict the collapse of overhangs.

  • Serial deposition and elastic deformation lead to unique deflection profiles.

  • Collapse and deflection models provide guidelines for feedstock design.

Abstract

Recent developments have enabled material extrusion additive manufacturing of thermoset-based composite inks on the large scale. In addition, printing out-of-plane components is of broad interest to the polymer material extrusion community. This work addresses some of the challenges associated with both large-scale and out-of-plane thermoset material extrusion additive manufacturing by studying the height at which thin overhanging walls collapse. Walls at a range of overhang angles were printed until they collapsed. An optical camera captured the profile of each wall throughout the print, allowing the collapse height to be identified and the geometric fidelity to the programmed angle to be evaluated. Using previously measured rheological properties, predictive models were generated to approximate the collapse height and profile of the deflected walls. First, an analytical model was created to predict the height at which the walls would yield. The analytical model assumes the walls exhibit a perfectly linear profile; however, experiments proved this assumption to be false. Therefore, a finite element simulation was developed to account for the elastic deflection that occurs during printing. The finite element simulation predicts both the yield height and the deflected profile after the deposition of each layer. For the properties of the thermoset ink used here, the yield height predicted by the analytical model and finite element simulation are virtually identical. These predictions match experimental data reasonably well, but minor errors are observed. Accounting for the fully plastic moment appears to explain the small mismatch between experimental data and predictions. Additionally, the finite element simulation provides an excellent prediction of the deflected profile before the wall begins to collapse. By demonstrating that the collapse height and deflected profile of thin overhanging walls can be predicted, this work illustrates how the soft viscoelastic properties of thermoset-based composite inks limit the scale of a key feature required to print some nonplanar components. It also provides a basis to tailor in-process curing systems to suppress deflection and collapse of thin overhanging walls.

Introduction

Large-scale polymer additive manufacturing has seen rapid development over the past ten years. In 2014, the Big Area Additive Manufacturing (BAAM) system revolutionized the size of parts that could be printed by material extrusion of thermoplastic polymers [1], [2]. The BAAM has inspired development of other large material extrusion printers like the Large Scale Additive Manufacturing (LSAM) system created by Thermwood [3] and the Large-Scale Bio-Based Additive Manufacturing system at the University of Maine [4]. In 2018, the Reactive Additive Manufacturing system was developed to print large-scale parts using thermoset-based composite inks [5], [6], [7]. When compared to thermoplastics, thermoset inks are expected to improve toolpath flexibility [7], [8], require less energy to achieve extrusion [8], [9], enhance interlayer bonding, reduce anisotropy, and show potential to increase print speed [9], [10], [11]. However, uncured thermoset inks are susceptible to the slumping [9], [12], [13], [14], [15], [16] and collapse [17], [18], [19] behavior observed in materials that rely on rheological properties to maintain structural stability under their own weight.

Several in-process reactive curing mechanisms exist to solidify the material and suppress these instabilities, including chemical initiation [5], [6], [9], [10], ultraviolet (UV) initiation [20], [21], [22], [23], and thermal initiation [24], [25], [26], [27]. The kinetics of these reactions can be tailored to keep pace with the print and maintain stability of a given structure. As a baseline to guide the design of the appropriate curing mechanism for a given structure, the stability of that structure in the absence of curing must be understood. Recent work revealed that rheological properties of an ink without its curing agent can be used in self-weight mechanical models to accurately predict the collapse height of thin, semi-infinite walls printed with such an ink [18]. This key finding suggests that the maximum stable height of other structures may be predicted to reasonable accuracy through simple mechanics models by assuming the complex, viscoelastic inks behave in an elastic-plastic manner. While the elastic-plastic assumption may seem severe, much of the prior effort in designing inks for material extrusion additive manufacturing (AM) has focused on achieving elastic-plastic-like behavior in suspensions or polymer resins, precisely because this behavior imparts stability to the printed object prior to drying or curing.

“Out-of-plane” printing has also gained attention in recent years. Developments have been made to print overhanging features without supports [16], [20], [23], [25], [28], [29], [30], structures on freeform surfaces [31], [32], [33], [34], [35], [36], and nonplanar components using machines with more than 3 degrees of freedom (DOF) [31], [37], [38], [39], like robotic arms [40], [41], [42], [43], [44]. Previous research has either been conducted on scales small enough to neglect self-weight loading or has focused on thermoplastics, which quickly solidify after deposition. Therefore, to the authors’ knowledge, the current literature has not rigorously analyzed the stability of thin overhanging walls printed with thermoset inks that rely solely on uncured rheological properties to support their own weight.

The present work studies the stability of thin overhanging walls printed with thermoset inks. An epoxy-based composite ink without a curing agent is used to probe the limits of stability in the absence of cross-linking or in situ gelation. Overhanging walls are printed in a layer-by-layer fashion at a range of angles and observed as they collapse. Predictions of the yield height based on classical beam mechanics and previously obtained rheological properties [18] are shown to be in good agreement with the collapse height observed in experiments. Since this model makes no assumptions about how material is deposited, it can be extended to analyze thin overhanging walls printed with a wide array of material extrusion approaches, including out-of-plane approaches that alter the approach angle of the extruder. A finite element (FE) model designed to account for the elastic deflection that occurs between the deposition of each layer is shown to accurately predict the deflected profile of the overhanging walls. Since these models only assume elastic-plastic behavior, they can be applied to a wide range of materials that exhibit such behavior. These design tools provide the information needed to tailor curing kinetics to suppress both collapse and elastic deflection of thin overhanging walls printed with thermoset inks.

An example that illustrates the utility of the understanding developed in this work is shown in Fig. 1a, which shows a honeycomb with walls normal to a curved surface. These conformal honeycombs are essential for aerospace components that require highly contoured sandwich panels, like leading edges, flaps, nacelles, support panels for heat shields, radomes, and other curved shapes [45], [46], [47]. Material extrusion AM could be used to increase design freedom of conformal honeycombs beyond current prefabricated options [45]. The work presented here builds a fundamental understanding needed to successfully use thermoset material extrusion to print the large-scale, out-of-plane, overhanging walls required for conformal honeycombs.

Section snippets

Material formulation

A thermoset composite ink was formulated following Romberg et al. [18] by adding 10 wt percent (wt%) fumed silica (Cab-o-sil TS-720, Cabot Corporation, Alpharetta, GA) to an epoxy resin (Epon 826, Momentive Specialty Chemicals, Inc. Columbus, OH) in several steps. 315 g of resin was added to a 750-cc mixing cup, then held in a 60 °C oven for two hours to melt any crystallized material. The resin was then allowed to cool to room temperature. Next, 8.75 g of fumed silica was added to the resin

Analytical self-weight yielding model

As has been noted in previous work [17], [18], [19], self-weight is a key factor affecting the stability of printed thermoset inks because they exhibit such low specific strength and stiffness. Therefore, a mechanical model that considers beam bending under self-weight loading was generated to predict the height at which these thin overhanging walls collapse. Additionally, a distributed load was included at the top of the wall to account for the force caused by deposition. This model assumes

Geometric fidelity

For each programmed α, Fig. 6 shows how the measured value of α evolved as new layers were deposited. For clarity, only one print is shown for each value of α. Early in the print, the measured value of α was noisy for all the prints due to the limitations of the color thresholding program. After layer 10, the measurement for all the prints stabilized to a plateau value of α. This plateau was longer and flatter for smaller values of α. This figure shows that the measured α did not match the

Limitations on geometric fidelity

The results revealed limitations on the geometric fidelity of printed overhanging walls. The measured α was generally less than the programmed α prior to collapse. Considering the way that beads compressed may explain these inconsistencies. Each layer of the walls consisted of four adjacent beads. Three of those beads landed directly on top of the previous layer, whereas the fourth bead made incomplete contact and was partially unsupported. This difference in boundary conditions caused the

Conclusion

To better understand how to print conformal structures on the large-scale (Fig. 1a), this work focused on expanding the understanding of the link between rheological properties and the structural stability of thermoset inks by modeling and printing thin overhanging walls with a material extrusion system. Thermoset inks were successfully printed at prescribed overhang angles up to 50°, and yield height predictions were generated with an analytical model and an FE model that used the shear yield

CRediT authorship contribution statement

Abir Abrian I.: Software, Data curation. Hershey Christopher J.: Supervision, Project administration, Funding acquisition. Kunc Vlastimil: Supervision, Resources, Project administration, Funding acquisition. Compton Brett Gibson: Writing – review & editing, Supervision, Resources, Project administration, Methodology, Funding acquisition, Conceptualization. Romberg Stian Kristov: Writing – original draft, Visualization, Validation, Supervision, Software, Methodology, Investigation, Formal

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, Industrial Technologies Program, under contract DE-AC05-00OR22725 with UT-Battelle, LLC. SKR would also like to acknowledge the generous support of the University of Tennessee and the University of Tennessee Tickle Fellowship. SKR would also like to thank Robert Cody Pack for his support in setting up the vision system used in this work. AIA and BGC would like to acknowledge support from

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      In AM, print quality, geometric resolution, and material performance are strongly dependent on the process parameters [11,12]. This is especially prevalent in extrusion AM when 3D printing thermoplastics [13,14], thermoset inks [15–17], soft materials [18–20], and other viscous inks [21,22]. During DIW, the process parameters include paste ink properties (e.g., viscosity, rheology, fiber loading, etc.) and manufacturing parameters (e.g., nozzle size and shape, print head speed, extrusion rate, etc.).

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    This manuscript has been authored in part by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).

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