Supporting information for Numerical investigation of the influence of process conditions on the temperature variation in fused deposition modeling

ZHANG, Jie1; WANG, Xin Zhou1; YU, Wang Wang1,2; DENG, Yu He1,3*

1. College of Materials Science and Engineering, Nanjing Forestry University, Nanjing 210037, China;2. School of Mechanical Engineering, Nanjing Vocational Institute of Industry Technology, Nanjing 210023, China3. Key Laboratory of Wood Science and Technology Zhejiang Province, Lin’an 311300, China.Correspondence to: Deng, Yu He (E-mail: dengyuhe@hotmail.com)

ContentsFigure S1. Physical properties of PLA--------------------------------------------------- Page S2Figure S2. Temperature field at characteristic time---------------------------------- Page S2Figure S3. Overall cooling rate and the related---------------------------------------- Page S3Figure S4. Thermal property revealed from differential scanning calorimetry and supporting discussion---------------------------------------------------

Page S3-S4Supporting discussion on the improvement of the modeling---------------------- Page S5References in supporting information-------------------------------------------------- Page S5

Readers can also go to GIF pictures included in the .pptx file for direct observation of the temperature field and temperature gradient intensity variation with respect to space at characteristic time in FDM.

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(a) (b)

Figure S1 Variation of density (a) and specific heat capacity (b) of PLA with respect to temperature. A shape-preserving piecewise cubic interpolation and extrapolation method is employed in the calculation. Variation of density of PLA with respect to temperature at atmospheric pressure is calculated as the reciprocal of specific volume from the pressure-volume-temperature relationship of the polymer [1]. The data in Figure S1(b) come from the recommended value in [2], with a slight modification at 180K from 61.40 to 64.40 J

K mol.

(a) (b)

(d)(c)

Figure S2. Temperature field at various moments. (a) t=1.01 tN; (b) t=1.1 tN; (c) t=1.5 t N; (d) t=2 tN.The directions shown by red arrows in the figure indicate the layer number in an ascending order, from the 1st layer to the 10th. When the time exceeds 1.5 tN, temperature field does not seem to vary intensively, indicating the steady state of the temperature field is S2

approached.

(a)

(b)

Figure S3. (a) A piece-wise fitting of mean temperature variation with respect to time during and after the FDM process; (b) variation of overall cooling rate with respect to time, β=β (t ), as a contrast to Figure 5(a), in which variation of overall cooling rate is displayed as a function of the mean temperature, β=β (T ).

Figure S4. Differential scanning calorimetry (DSC) curves of different PLA-related materials at different cooling rates.There are two compositions, namely, pure PLA (3052D) and PLA+3% talc

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(a kind of inorganic nucleating agent), subjected to two different cooling rates β=10℃ /min and β=5℃ /min, respectively. All the specimen used in the DSC test were previously heated from 20℃ to 200℃, maintained at 200℃ for 5 mins, and then cooling accordingly, the curves are shown in Figure S4. All measurements were performed on a DSC6100 (NETZSCH-Gerätebau GmbH, German) machine in the nitrogen atmosphere, using approximately 5-10 mg of tested sample of different compositions. As shown, when neat PLA was cooled down at a rate of (or higher than) β=10℃ /min, crystallization of the semi-crystalline polymer from polymer during such cooling process is insignificant; when the cooling rate was milder, e.g. at β=5℃ /min, crystallization phenomenon is significant, with onset and end temperature of crystallization of 106.2℃ and 84.9℃, peaking at 96.6℃ and a peak width of 16.5℃. Thus, a threshold of cooling rate of β=10℃ /min for semi-crystalline polymer PLA (3052D) is detected in cooling process, above which crystallization will not happen during FDM.When PLA was incorporation with 3% talc, the crystallization phenomenon was more profound. Not only did the crystallization behavior change, but also the degree of crystallization. The heat released from such crystallization process was estimated to be Qc=−34.0 J / g, with a degree of crystallinity χc=36.3%. While the overall heat dissipation of PLA in FDM is

Q=∫200

20

c p(T )d T=−349.6 J / g,¿Qc∨

¿¿Q∨¿≈10% .¿

¿ Ignoring the influence of phase transition, the simulated temperature field will be significantly lower than the real value, especially in the region below temperature of crystallization T c. Given modified chemical composition, purity, molecular weight, thermal history and crystallization condition of PLA, the heat released from phase transition could be more significant [3].Improvement of the modeling

As indicated in the hypothesis and modeling section of the main manuscript, this mathematical model could be further improved at least from the following aspects:Influence of raster angle and filling ratio.This model is developed under constant raster and filling ratio. These two parameters have significant influence over the thermal process in FDM, and should be studied in further research. In essence, a different raster angle only plays the role of allocation of different types of boundary to different elements deposited, but a different filling ratio would completely change the S4

heat transfer problem in solid to one in porous media, which is much more complicated given any designed porosity and permeability.Hypothesis 1 could be excludedHypothesis 1 is assumed because most widely used polymers in FDM include amorphous thermoplastic (acrylonitrile-butadiene-styrene, ABS) and semi-crystalline plastic (PLA). For amorphous polymer, the influence of phase transition on temperature is insignificant. For semi-crystalline polymer, in the usual case of rapid cooling in FDM, the macromolecules of the polymer cannot form crystalline structures even though the polymer is inherently crystallizable. However, if cooling rate is well controlled, especially in the case of nucleating agent incorporation, the heat released from crystallization of polymer melt could be significant compared with overall heat dissipated. Ignoring the influence of phase transition, the simulated temperature field would be significantly lower by more than 10%, especially in the region below temperature of crystallization T c (Figure S4). However, to exclude hypothesis 1 in the modeling, a complete understanding of polymer crystallization thermodynamics and kinetics is a prerequisite, which is still an on-going research subject.Boundary conditionBoundary conditions could be modified to the Type 3, to include the influence of heat radiation and convection in heat transfer in detail. This is of practical importance when polymer of high melting point or metal alloy is employed in FDM (e.g. the melting temperature of PEEK is ~600℃ [4]). By adjusting the coefficient of heat convection, the influence of turning on/off the fan attached to the printing nozzle can also be investigated.References in supporting information1. L.T. Sin, A.R. Rahmat, W.A. Rahman, Polylactic Acid: PLA Biopolymer Technology and Applications, William Andrew, 2012, chapter 3.2. M. Pyda, R. Bopp, B. Wunderlich, Heat capacity of poly (lactic acid). J. Chem. Thermodyn. 36(9)(2004) 731-742. http://dx.doi.org/10.1016/j.jct.2004.05.0033. R. Auras, L.T. Lim, S.E.M. Selke, H. Tsuji, Poly(lactic acid): Synthesis, Structures, Properties, Processing and Applications, Wiley, 2010, chapter 9.4. W. Wu, P. Geng, G. Li, D. Zhao, H. Zhang, J. Zhao, Influence of layer thickness and raster angle on the mechanical properties of 3D-printed PEEK and a comparative mechanical study between PEEK and ABS, Materials. 8(9)(2015) 5834-5846. DOI:10.3390/ma8095271

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