Characterization of resistors created by fused filament fabrication using electrically-conductive filament

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28th International Conference on Flexible Automation and Intelligent Manufacturing 28th International ConferenceJune on Flexible Automation and OH, Intelligent (FAIM2018), 11-14, 2018, Columbus, USA Manufacturing (FAIM2018), June 11-14, 2018, Columbus, OH, USA

Characterization of resistors created by fused filament fabrication Characterization of resistors createdConference by fused filament fabrication Manufacturing Engineering Society International 2017, MESIC 2017, 28-30 June using electrically-conductive filament 2017, Vigo (Pontevedra), Spain using electrically-conductive filament Nebojsa I. Jaksica,* and Pratik D. Desaib a,* b Costing models forNebojsa capacity optimization in Desai Industry 4.0: Trade-off I. Jaksic and Pratik D. Colorado State University – Pueblo, 2200 Bonforte Blvd. Pueblo, CO 81001, USA between capacity and operational efficiency Riceused Lake Weighing Systems, 230 2200 W. Coleman St.Blvd. Rice Pueblo, Lake, WICO 54868, USA Colorado State University – Pueblo, Bonforte 81001, USA a

a

b

b

Rice Lake Weighing Systems, 230 W. Coleman St. Rice Lake, WI 54868, USA

A. Santanaa, P. Afonsoa,*, A. Zaninb, R. Wernkeb Abstract a University of Minho, 4800-058 Guimarães, Portugal Abstract b Unochapecó, 89809-000 Chapecó, SC, Brazil Desktop fused filament fabrication (FFF) printers (3D printers) are ubiquitous rapid prototyping (RP) and additive manufacturing (AM) devices by small and large companies wellprinters) as by hobbyists. Their attractiveness stems from theadditive inexpensive hardware, Desktop fusedused filament fabrication (FFF) printersas(3D are ubiquitous rapid prototyping (RP) and manufacturing inexpensive materials, CAD environments, and short Their training times. Thisstems research design ofhardware, resistors (AM) devicesplastic used by small andaffordable large companies as well as by hobbyists. attractiveness fromexplores the inexpensive created by the FFFmaterials, printing affordable process using carbon explores black and graphene-based inexpensive plastic CADcommercially environments,available and shortelectrically-conductive training times. This research design of resistors Abstract filament.by3Dthe printed resistors process are designed, andavailable characterized. A number of tests carbon are performed resulting in a set of created FFF printing usingconstructed, commercially electrically-conductive black and graphene-based build recommendations. thisdesigned, novel capability to directly create will electrical components integrated into 3D printedinphysical filament. 3D concept printed resistors are constructed, and characterized. A of to testsbe areincreasingly performed resulting a set of Under the of With "Industry 4.0", production processes benumber pushed interconnected, objects designers canonenvision and novel 3D print newnecessarily, and/or improved devices with embedded electronics, which couldphysical not do build recommendations. capability to directly create electrical components integrated 3Dthey printed information based aWith real this time basis and, much more efficient. In this context, into capacity optimization before. objects designers can envision and 3D print new and/or improved devices with embedded electronics, which they could not do goes beyond the traditional aim of capacity maximization, contributing also for organization’s profitability and value. before. Indeed, lean management and continuous improvement approaches suggest capacity optimization instead of © 2018 The Authors. Published by Elsevier B.V. maximization. The study of capacity optimization and costing models is an important research topic that deserves © 2018 2018 The Authors. by B.V. This is an open accessPublished article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) © The Authors. Published by Elsevier Elsevier B.V. This is an openfrom accessboth article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/) contributions the practical and theoretical perspectives. This paper presents discusses a mathematical Peer-review under responsibility of the CC scientific committee of the 28th Flexible Automation andand Intelligent Manufacturing This is an open access article under BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility ofbased the scientific committee of the 28th (ABC Flexible Automation and Intelligent Manufacturing model for capacity management on different costing models and TDABC). A generic model has been (FAIM2018) Conference. Peer-review responsibility of the scientific committee of the 28th Flexible Automation and Intelligent Manufacturing (FAIM2018)under Conference. developed and it was used to analyze idle capacity and to design strategies towards the maximization of organization’s (FAIM2018) Conference.

value. The trade-off capacity3Dmaximization vs filament, operational is highlighted and it is shown that capacity Keywords: additive manufacturing, printing, conductive fused efficiency filament fabrication, FFF Keywords: additive manufacturing, 3D printing, conductive filament, fused filament fabrication, FFF optimization might hide operational inefficiency. © 2017 The Authors. Published by Elsevier B.V. 1. Introduction Peer-review under responsibility of the scientific committee of the Manufacturing Engineering Society International Conference 1. Introduction 2017.

Rapid prototyping (RP), commonly known as three dimensional (3D) printing is a form of additive manufacturing

Keywords: Cost Models; ABC; TDABC; Capacity Management; Idle Capacity; Operational Efficiency Rapid prototyping (RP), commonly known three dimensional (3D) printing a form of additive (AM) process that builds objects layer by layer.asThe first AM process was createdisby Charles W. Hull manufacturing in 1986. Since

(AM) process that builds objects layer by layer. The first AM process was created W.designers Hull in 1986. the product development phase usually includes multiple design iterations, prior toby 3DCharles printing, had toSince wait the product development phase usually includes multiple design iterations, prior to 3D printing, designers had to wait many weeks to receive a prototype from the fabrication facility. Nowadays, 3D printing is accepted as a preferred 1. Introduction many weeks to receive a prototype from the fabrication facility. Nowadays, 3D printing is accepted as a preferred

2351-9789 © 2018 Thecapacity Authors. Published by Elsevier information B.V. The cost of idle is a fundamental for companies and their management of extreme importance This is an open access under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) 2351-9789 © 2018 Thearticle Authors. Published by Elsevier B.V. in modern production systems. In general, it is defined as unused capacity or production potential and can be measured Peer-review under responsibility of the CC scientific committee of the 28th Flexible Automation and Intelligent Manufacturing (FAIM2018) This is an open access article under BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) in several ways: tons of production, available hours of manufacturing, management of (FAIM2018) the idle capacity Conference. under responsibility of the scientific committee of the 28th Flexible Automationetc. Peer-review and The Intelligent Manufacturing * Paulo Afonso. Tel.: +351 253 510 761; fax: +351 253 604 741 Conference. E-mail address: [email protected] 2351-9789 Published by Elsevier B.V. B.V. 2351-9789©©2017 2018The TheAuthors. Authors. Published by Elsevier Peer-review underaccess responsibility the scientific committee oflicense the Manufacturing Engineering Society International Conference 2017. This is an open article of under the CC BY-NC-ND (http://creativecommons.org/licenses/by-nc-nd/3.0/) Peer-review under responsibility of the scientific committee of the 28th Flexible Automation and Intelligent Manufacturing (FAIM2018) Conference. 10.1016/j.promfg.2018.10.010

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method for production of functional prototypes and small batches because they can be created in a matter of hours. Also, some geometric features of objects can only be created by using AM (e.g. honeycomb internal object structures). The overall objective of this research is to further the field of 3D printing by introducing new commercially available electrically conductive filament for fused filament fabrication (FFF) 3D printers and by designing and creating 3D printed passive electrical components like resistors. Printing usable circuits using biodegradable electrically conductive filament offers a benefit to the user and the environment. Being able to 3D print entire electrical circuits within 3D printed object allows designers to better integrate electrical components within physical objects. With the recent developments in 3D printers and conductive 3D printing materials, there is a window of opportunity to design/create/produce entire electrical circuits within designed 3D printed objects thus achieving a new level of design integration. In the past few years, some research focused on the use of electrically-conductive materials as filament in 3D printers for creation of conductive traces (like the traces on printed circuit boards) so that they can be embedded into 3D printed objects. While there is significant research on conductive materials, these materials are not readily accessible. Currently, only electrically-conductive plastic composite filaments based on carbon black and graphene are commercially available for consumer grade FFF 3D printers. To achieve a higher level of integration between electrical and mechanical components of 3D printed objects, there is a need to design, create, and characterize electrical components made of conductive materials. This work provides guidelines for creation of electrical elements within objects as they are 3D printed, thus providing an additional functionality (another dimension) to these objects (often referred in the 3D printing literature as 4D objects). 2. Previous work and state of the art Scott Crump invented FFF in 1989 [1]. Many consider the expiration of his U.S Patent 5,121,329 [1], and other patents related to FFF as key to the steep growth of inexpensive FFF 3D printers [2]. Also, there has been a considerable effort to develop 3D printers for printing electronics, mostly at the printed circuit board (PCB) levels. For example, Voxel8 created a FFF 3D electronics printer with two nozzles capable of extruding PLA and proprietary silver-based conductive ink [3]. Nano Dimension’s DragonFly 2020 3D printer uses inkjet deposition, to produce multilayer printed circuit boards (PCBs) [4]. Electrically conductive polymer composites have been studied extensively [5 - 7]. Trihotry et al [8] study the effect of curing on dielectric properties of carbon black – epoxy composites (binary composite) while Zhang et al [9, 10] study composites of carbon black and silica in an epoxy resin matrix (tertiary composite). Liu and Choi [11] study resistance of multiwall carbon nanotubes (MWCNTs) - poly(dimethylsiloxane) (PDMS) composite under tensile strain while Hu et al [12] study strain sensors made of MWCNTs-epoxy composites. Chandrasekaran et al [13] show that graphite nano-platelets in epoxy resin as a matrix exhibit low 0.3 wt.% percolation threshold (filler-to-matrix ratio causing a composite to abruptly change from an isolator to a conductor). Mohan et al [14] describe electrical characteristics of graphene-based composites. Conductive material advancements for 3D printing include Leigh et al. [15] who formulated a conductive thermoplastic composite “carbomorph”, and used it in an inexpensive FFF multi-extruder 3D printer to create functional objects like sensors [16]. The carbomorph is created using Carbon Black (CB) as a filler to provide conductivity, and is mixed with polycaprolactone (PCL). The measured resistivity of 3D printed 5 mm cubed blocks was 9.0±1.0 Ω-cm, and 12.0±1.0 Ω-cm for in-plane and perpendicular to the layers, respectively. However, further research is required to investigate if resistivity is maintained with changes of the block size in the x, y, and z directions. To make functional 3D printing accessible, a commercially available conductive filament is required. At the time of this writing, one of the two most popular thermoplastics used as filaments for FFF printers is Polylactic acid (PLA). Just like PCL, PLA has the advantage of being biodegradable. Also, ProtoPlant offers Proto-pasta conductive PLA that uses CB as the conductive material [17]. It offers volume resistivity for in-plane and perpendicular to the layers, of 30 Ω-cm and 115 Ω-cm respectively. Black Magic 3D offers conductive graphene filament that uses graphene as the conductive material [18]. Black Magic 3D claims a volume resistivity of 0.6 Ω-cm which is significantly lower than the resistivity of conductive PLA from Proto-pasta. However, for either material it is not clear what testing methods and equipment is used to calculate their respective resistivities.



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3. Research Methodology This section details the experimental methods and processes used to effectively characterize passive elements. Where possible, a clear set of guidelines have been extracted from current standards. These guidelines form the basis for the experimental process, data collection, and evaluation undertaken in this work. In any engineering related process, the use of global standards promotes efficient development of technology while minimizing duplication of effort. In 2009, the American Section of the International Association for Testing Materials (ASTM), formed committee F42 on additive manufacturing technologies [19]. Soon after their formation, the committee completed the Terminology Standard. In October 2011, the International Organization for Standards (ISO) and ASTM decided to combine their efforts on AM, by forming a collaboration between the ISO Technical Committee 261 and ASTM International Committee F42. In 2013, the joint committee published ISO/ASTM 52900:2013 “Additive manufacturing — General principles — Terminology”. According to the standard ISO/ASTM 52900:2015, there are seven families of additive manufacturing listed in the terminology section [20]. One of these families is material extrusion which includes FFF. However, these standards do not address measurement and analysis of electrical resistance, capacitance, and inductance of 3D printed objects. Thus, for the purpose of this research, current industry standards are used to extract a process for effective characterization of 3D printed resistors. The standard ASTM D4496 – 13 titled “Standard Test Method for D-C Resistance or Conductance of Moderately Conductive Materials”, is an industrial standard used for measuring direct current (DC) resistance of resistive materials [21]. The standard describes a test method that can be used to attain accurate resistance measurements. As such, this standard is evaluated to form a set of procedures to be used for attaining resistance data from the 3D printed test samples. The scope section of the D4496 states that the test method is applicable to all material that have a volume resistivity in the range of 1 to 107 Ω-cm. The manufacture of conductive PLA states the volume resistivity of 3D printed parts from conductive PLA are roughly in the range of 30-150 Ω-cm [17]. The manufacturer of graphene PLA states the volume resistivity of solid piece of material at 0.6 Ω-cm, which falls below the minimum volume resistivity requirement for the application of D4496 [18]. However, material extrusion 3D printers produce internally nonhomogeneous parts due to infill variations. As such, the volume resistivity of as-printed graphene PLA is assumed to be higher than the stated 0.6 Ω-cm, once printed using a material extrusion 3D printer. Thus, it is assumed that 3D printed parts using conductive PLA and graphene PLA will fall within the range of volume resistivity as defined by D4496. Applied measurement and reporting procedures satisfy D4496 standard and are here incorporated by reference. Instruments used for resistance measurements were a Fluke 73, Fluke 3000 FC, and an NI Elvis Workstation. Since the manufacturers did not provide filler loading for either of the two composites, thermo-gravimetric analysis (TGA) using a TGA 550 by TA instruments was used to measure the amount of CB and graphene. Filament samples as well as virgin PLA samples were analyzed using a temperature ramp heating at 10 °C/min from 40 °C to 800 °C. Samples contained 26 wt. % of CB and 16 wt. % graphene, respectively, which is well above their percolation thresholds as reported in the literature. 4. FFF 3D Printer improvements A MakerBot® Replicator 2X Experimental 3D printer (2X) is exclusively used for all 3D prints created in this work [22]. The 2X is a dual extruder 3D printer which can extrude two filaments during a single print cycle. This provides a means to create electrical circuits on top, or within an insulating material extruded by the second extruder. The inside cavity of the printer is referred to as the build chamber. Within the build chamber resides the heated build platform. Kapton® tape is applied to the build surface to improve the adhesion and release of printed objects. Filament enters at the top of the extruder assembly via plastic hollow guide tubes, passes through the heater core and is extruded via the nozzles underneath. Towards the rear of each extruder there is a stepper motor driving a micro-toothed pinion wheel to feed and retract filament. Towards the front are fans coupled to heatsinks, keeping the extruder assembly from overheating due to the high temperatures of heater cores. Overheating of the extruder assembly causes filament to prematurely soften, making the extrusion process inconsistent. The 3D printing software chosen for this work is the MakerBot Desktop because it is freely available by the manufacturer and has ongoing customer support. This proprietary software (a 3D printing graphical user interface)

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accepts .stl files of objects that can be combined with other objects for printing. Objects can be moved, rotated, and scaled. Many printing parameters can be adjusted (nozzle and bed temperature, nozzle travel speed, number of shells, extrusion speed, filament cooling fan speeds, infill height and pattern, raft and supports). To adjust the MakerBot 2X to print with PLA, the heated build platform is set to 70°C in software. This temperature along with the Kapton tape, provides the best condition for printing the first layer of objects. Extruders are set to 230° C. A filament lubricator is added with an inserted sponge lightly coated with Canola cooking oil [23]. This provides additional lubrication for the PLA filament as it enters the heating core. This modification dramatically reduced the rate of clogged nozzles. Next, the print quality of the 2X is optimized. First, the 2X was calibrated as suggested by MakerBot. To measure the print quality of the printer, a standardized test was downloaded from Thingiverse [24]. Then, two printer modifications were applied. The first modification to the 2X was an extruder drive block upgrade [25]. The upgrades were printed using standard ABS filament, which replaced the standard extruder parts. This upgrade helped improve the consistency of prints due to reduced slippage of the stepper motor pinion gear. The next modification to the 2X was an attachment of two additional cooling fans [26], one for each extruder, actively cooling extruded molten filament. Fig. 1 (a) shows the 3D print created with standard 2X, while Fig.1. (b) shows the improved 3D print.

a

b

Fig. 1. Standard 2X test print: (a) before the improvements; (b) after the improvements

5. Characterization of resistors In this section, resistors are designed and characterized. For each element, resistivity is analyzed in X, Y, and Z axis with reference to the MakerBot 2X build platform. Resistors are printed on testing platforms, or testbeds. The testbeds provide structural rigidity, as well as an insulating platform for electrical isolation between resistors. From preliminary tests, a base thickness of 1 mm was selected for optimal rigidity while minimizing the amount of PLA. Manufacturers of conductive PLA list resistivity of their material for a given volume of uniform density. The uniform density of the material is critical to give resistance values with low tolerances. However, due to the 3D printing process, a uniform structure is not produced. 3D prints can vary in the levels of adhesion between layers along the Z-axis, as well as have internal air gaps within the printed structure. Furthermore, the extruded filament can be non-uniform and incur breaks during extrusion caused by various factors. These inconsistencies during the 3D printing process can result in variations in the volume resistance ሺܴ௩ ሻ in a 3D printed resistor. These variations caused by FFF printing technology need to be characterized, so that designers can effectively implement resistors in their designs. 5.1. Design of resistors A cuboid shape is selected to form the resistor sample to fully characterize the effects on resistance from an individual axis. The cuboid shape allows for the width, length, and height to be changed which in turn corresponds to the X, Y, and Z axis of the MakerBot 2X build chamber. Fig. 2 (a) shows the resistor test sample design. This design is created in Autodesk Inventor® CAD software. The test sample consists of a resistive cuboid element with two electrode contact pads placed at each end. To integrate 3D printed circuits with external components such as LEDs, a suitable contact point has to be provided. The 3D printed contact point should provide sufficient rigidity to secure external components while minimizing contact resistance. Due to the resistive property of the conductive filament, contact resistance plays a significant role in determining the final volume resistance ሺܴ௩ ሻ of the test sample. It is for these reasons that contact pads are added to the test sample. Each contact pad is a cylinder of 5 mm in diameter, having the same thickness as the resistive cuboid. On the top surface of the contact pad, silver based conductive paint is



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applied to minimize the contact resistance. The contact pad once covered with conductive paint, provides a uniform resistive area when performing resistance measurements. 5.2. Resistance versus x-axis expansion To characterize the change in volume resistance ሺܴ௩ ሻ of conductive PLA along the X-axis, the following testbed with six resistors depicted in Fig. 2 (b) is created. The width of each resistor sample along the x-axis is increased in 0.4 mm increments, starting from 0.8 mm and ending with 2.4 mm. In all resistor samples, the cross-sectional height is kept constant at 1.0 mm, along with a constant length of 30.0 mm. As test specimens are placed closer to each other, the likelyhood of electrical shorts between them increases. These shorts occur during the printing phase of nonconductive layers due to the extruder leaking small amounts of conductive filament. The leaked conductive filament is smeared on to the non-conductive gaps inbetween the conductive test specimens. This smearing effect dramatically increases the likelyhood of shorts when the spacing is set to 2.0 mm or less. As such, a minimum spacing of 5.0 mm is provided between resistor test specimens.

a

b

Fig. 2. (a) Resistor Test Sample Design (mm); (b) 3D printed sample of an x-axis expansion testbed

A redundant resistor sample whose value is not measured, is placed towards the right most position along the xaxis. During initial print testing on MakerBot 2X, it was observed that once the non-conductive testbed was printed, the conductive PLA extruder had inconsistent starts when extruding the first few centimeters of filament. It was also observed that while printing the first conductive layer, the right most resistor sample’s first layer was printed first. Due to these combined effects, the right most resistor produced inconsistent resistance data. Therefore, an additional resistor is placed in the right most position along the x-axis on the test plate, and rejected during data collection. The slicer software creates a single shell wall around the perimeter of the resistor test samples. Due to the first sample’s resistive element having a width of 0.8 mm (2 times the nozzle diameter), the slicer simply creates a single shell wall without infill. However, as the width of resistive element increases for subsequent test samples, the slicer adds infill for any gaps created in between the single shell wall. This is a process variation and may result in a change in volume resistivityሺߩ௩ ሻ. In Fig. 3 (a) the resistance data for each print is plotted against the width of the resistive elements. As per expectation, the resistance is decreasing with the increase in the width of the resistive element. The volume resistivityሺߩ௩ ሻ has been plotted in Fig. 3 (b). There is a significant jump in volume resisitivity with an increases in width from 0.8 mm to 1.2 mm. This increase in resistivity is expected due to the addition of infill within the resistive element when width is 1.2 mm or greater. At the width of 0.8 mm, the resisitive element consists only of two outer shell layers. There is only a single filament to filament bond running along the y-axis, along the length of the resistive element. The lack of infill produces a resistive element with minimum amount of gaps, as well as reduces the filament to filament bonds, reducing overall resistivity. The addition of infill for resistive element of widths 1.2 mm and above increases resistivity. This is due to significant increase in filament to filament bonds as the direction of subsequent layers of infill are rotated 90° with respect to each other. This creates weak filament to filament bonds and as such increases resistivity. This characteristic

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of 3D printed resistors can be used as a design parameter when creating resistors using 3D printers. The resistance can be controlled in part by changes in infill directions and number of shell layers. Print 1

Print 2

Print 3

Print 4

Resistivity (Ω-cm)

2000 Resistance (Ω)

6.0

Print 5

1500 1000 500 0

5.5 5.0 4.5 4.0

0.8

1.2

1.6 Width (mm)

2.0

2.4

0.06

0.11

0.16

0.21

0.26

Width (cm)

Fig. 3. (a) Resistance vs. width (conductive PLA), height 1 mm, length 30 mm; (b) resistivity vs. width

5.3. Resistance versus y-axis expansion To characterize the change in resistance of conductive PLA along the Y-axis, a testbed with five resistor test samples is created. The resistor test samples range from 3 cm to 7 cm in increments of 1 cm in lenght along the Yaxis. In all resistor test samples, the cross-sectional height and width is kept constant at 1 mm and 0.8 mm, respectively. The height is set to 1 mm as it is evenly divisible by the layer height of 0.2 mm, as set in the MakerBot Desktop slicing parameters. Likewise, the cross-sectional width of resistors is set to 0.8 mm as it is evenly divisible by the extruder nozzle diameter of 0.4 mm. It is important to keep these parameters evenly divisible by their minimum alowable set values to reduce any bias effects caused from different slicing software. Furthermore, the cross-sectional height and width of resistors is kept to a minimum while producing a strong structural resistor that can widhstand normal wear and tear during the testing phase. This testbed omits the use of the redudandant resistor used in the previous testbed due to inconsistent extruder start. MakerBot Desktop slicing software offers a feature called purge wall which creates a wall of filament on the perimeter of the printed object. Although wastefull, prior to printing of any layer of the testbed, the purge wall layer was printed first. This eliminated the inconsistent extruder starts as the extruders get pre-charged with material. The purge wall also provides a barrier to trap unwated filament that may leak from the extruders. Fig. 4 (a) shows a plot of resistance vs. length data collected from the testbed. As expected, the average resistance increases with the increase in length of the resistive element. The standard deviation for all the tested lengths is within 4 % of the mean. However, somewhat unexpectedly, the plot shows that at the length of 5 cm, the overal resistance is slightly less than what is expected. To further analyze the data, resistivity values of the resistor samples are calculated. The calculated means are used as volume resistances for their respective lengths. The calculated resistivity values vs. resistor lengths are plotted in Fig. 4 (b). The plot in Fig. 4 (b) shows a dip in resistivity of 3.477 Ω-cm for sample length of 5 cm, placed in the center of the testbed. The adjacent samples of lengths 4 cm and 6 cm, have a higher resistivity of 3.642 Ω-cm and 3.730 Ω-cm, respectively, while the outer samples of length 3 cm and 7 cm, exhibit the highest levels of resistivity at 3.733 Ω-cm and 4.055 Ω-cm, respectively. This interesting material behavior with respect to resistivity can be explained as follows. The MakerBot Desktop slicing software slices the testbed and produces a set of instructions that are optimized for the path the extruder takes. Once the insulating platform is printed, the first layer of the right most resistor sample is printed. In this case the resistor sample with the length of 7 cm. This is followed by printing of first layers of resistor samples of length 6 cm, 5 cm, 4 cm, and finally 3 cm. For the second conductive layer, the 3 cm resistor sample is printed first, followed by 4 cm, 5 cm and so forth. The process then repeats itself. This however creates an inconsistency for the time intervals between subsequent conductive layers printed for each resistor sample. The different time intervals allow for inconsistent cooling of the previously extruded conductive layer, therefore, affecting the quality of adhesion for the subsequent conductive layer. The 5 cm resistor sample, due to its central position has the most consistent time intervals



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between additional conductive layers, whereas the outer resistor samples have two different time intervals, the shortest as well as the longest. Thus, the 5 cm resistor sample has the lowest volume resistivity. Print 2

Print 3

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Print 5

Resistivity (Ω-cm)

Resistance (Ω)

Print 1

4000 3000 2000 1000 0 3.0

4.0

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Length (cm)

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4.1 4.0 3.9 3.8 3.7 3.6 3.5 3.4 3.0

4.0

5.0

6.0

7.0

Length (cm)

Fig. 4. (a) Resistance vs. Length (Conductive PLA), height 1 mm, width 0.8 mm; (b) resistivity vs. length

To test the assumption of inconsistent time intervals between additions of conductive layers as the cause to inconsistent resistivity data, all the testbeds are heated in an oven to a temperature of 90°C (past the PLA glass temperature) for 10 minutes. The resistance in all samples has been reduced, but, the spread in the data has increased. 5.4. Resistance versus z-axis expansion To characterize the change in resistance of conductive PLA along the z-axis, two testbeds are created. The first testbed linearly increments height of resistor samples across the z-axis. The second testbed increments the height geometrically, using a common multiple of two. The two testbeds have been devised to provide additional data for the z-axis, as any change in the height of resistor sample results in different number of conductive PLA layers. This, layer to layer, bond is relatively weak and as such could vary the resulting resistance significantly. For the first testbed, the height of resistor samples from left to right along the x-axis, is increased from 0.1 cm to 0.5 cm in 0.1 cm increments. The resistive element width and length are kept constant at 0.8 mm and 30 mm, respectively. These values are selected to create at least one sample resistor that will overlap both testbeds. In this case it is the leftmost resistor sample with the height of 0.1 cm. The height values for the second testbed are (from left to right along the x-axis) 0.1 cm, 0.2 cm, 0.4 cm, 0.8 cm, and 1.6 cm. Since the data of the second testbed include a larger range of sample heights, resistance and resistivity vs. height are plotted in Fig. 5. The resistor sample data is plotted in Fig. 5 (a). The data points for each of the tested resistor heights are tightly grouped. As expected, the plotted data forms an exponential decay curve. The data plotted in Fig. 5 (b) shows a steady increase in resistivity. Here, one can see a linear progression of resistivity with the geometric increase in resistor sample height. A line of best fit is created, resulting in Equation 1,

�� = �1.9961 ∗ ℎ� + 3.3954

(1)

Where, ��� = Volume resistivity (Ω-cm) and ℎ = Height of resistor (cm).

6. Summary and Conclusions

Creating 3D printed objects with embedded 3D printed electronic circuits is a reachable goal for FFF 3D printers using electrically-conductive filament. In this work, the simplest electrical passive element, the resistor, is addressed. Due to the nature of the FFF process, the resistors created using graphene-based filament are non-homogeneous devices, thus their resistivity varies depending on their build orientation and FFF process parameters. An FFF printer, with two extruders and associated software was used to build a number of resistors for their characterization. Resistor expansions in x axis resulted in increased resistivity, but this increase was not linear. For z-axis expansions, the resistivity increase was mostly linear. The resistivity vs. length graph for y-axis expansion exhibited a minimum value in the middle of the test range. This work provides a number of guidelines and recommendations for designing 3D printed resistors as parts of 3D printed objects that contain electrical circuits.

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Print 2

Print 3

Print 4

Resistivity (R.(A/t)) (Ω-cm)

Print 5

2000 1000 0 0.1

0.2

0.4 Height (cm)

0.8

1.6

Resistivity (Ω-cm)

Resistance (Ω)

Print 1

Linear (Resistivity (R.(A/t)) (Ω-cm))

8.0 3.0 y = 1.9961x + 3.3954 0.0 0.5 1.0

1.5

2.0

Height (cm)

Fig. 5. (a) Resistance vs. height (Geometric) (C. PLA), width 0.8 mm, length 30 mm; (b) resistivity vs. height

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