{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T02:22:56Z","timestamp":1772850176059,"version":"3.50.1"},"reference-count":36,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,2,1]],"date-time":"2021-02-01T00:00:00Z","timestamp":1612137600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computers"],"abstract":"<jats:p>Additive Manufacturing Techniques such as Fused Filament Fabrication (FFF) produce 3D parts with complex geometries directly from a computer model without the need of using molds and tools, by gradually depositing material(s), usually in layers. Due to the rapid growth of these techniques, researchers have been increasingly interested in the availability of strategies, models or data that may assist process optimization. In fact, 3D printed parts often exhibit limited mechanical performance, which is usually the result of poor bonding between adjacent filaments. In turn, the latter is influenced by the temperature field history during deposition. This study aims at evaluating the influence of the phase change from the melt to the solid state undergone by semi-crystalline polymers such as Polylactic Acid (PLA), on the heat transfer during the deposition stage. The energy equation considering solidification is solved analytically and then inserted into a MatLab\u00ae code to model cooling in FFF. The deposition and cooling of simple geometries is studied first, in order to assess the differences in cooling of amorphous and semi-crystalline polymers. Acrylonitrile Butadiene Styrene (ABS) was taken as representing an amorphous material. Then, the deposition and cooling of a realistic 3D part is investigated, and the influence of the build orientation is discussed.<\/jats:p>","DOI":"10.3390\/computers10020019","type":"journal-article","created":{"date-parts":[[2021,2,1]],"date-time":"2021-02-01T11:40:48Z","timestamp":1612179648000},"page":"19","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["The Effect of a Phase Change on the Temperature Evolution during the Deposition Stage in Fused Filament Fabrication"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5980-5303","authenticated-orcid":false,"given":"Sidonie F.","family":"Costa","sequence":"first","affiliation":[{"name":"Center for Research and Innovation in Business Sciences and Information Systems (CIICESI), School of Management and Technology, Porto Polytechnic Institute, 4610-156 Felgueiras, Portugal"}]},{"given":"Fernando M.","family":"Duarte","sequence":"additional","affiliation":[{"name":"Institute for Polymers and Composites (IPC), Department of Polymer Engineering, University of Minho, 4804-533 Guimar\u00e3es, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0790-5801","authenticated-orcid":false,"given":"Jos\u00e9 A.","family":"Covas","sequence":"additional","affiliation":[{"name":"Institute for Polymers and Composites (IPC), Department of Polymer Engineering, University of Minho, 4804-533 Guimar\u00e3es, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,1]]},"reference":[{"key":"ref_1","unstructured":"Gebhardt, A. (2008). Understanding Additive Manufacturing: Rapid Prototyping\u2013Rapid Tooling\u2013Rapid Manufacturing, Hanser. [1st ed.]."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Chua, C.K., Leong, K.F., and Lim, C.S. (2010). Rapid Prototyping: Principles and Applications, World Scientific. [3rd ed.].","DOI":"10.1142\/6665"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1108\/13552540910979794","article-title":"Rapid prototyping\u2014A technology transfer approach for development of rapid tooling","volume":"15","author":"Ingole","year":"2009","journal-title":"Rapid Prototyp. J."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"433","DOI":"10.2174\/1381612822666161026162707","article-title":"Application of Fused Deposition Modelling (FDM) Method of 3D Printing in Drug Delivery","volume":"23","author":"Long","year":"2017","journal-title":"Curr. Pharm. Des."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Harris, M., Potgieter, J., Archer, R., and Arif, K.M. (2019). Effect of material and process specific factors on the strength of printed parts in fused filament fabrication: A review of recent developments. Materials, 12.","DOI":"10.3390\/ma12101664"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1549","DOI":"10.1122\/1.5037687","article-title":"The importance of rheological behavior in the additive manufacturing technique material extrusion","volume":"62","author":"Mackay","year":"2018","journal-title":"J. Rheol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/j.matdes.2009.06.016","article-title":"Parametric appraisal of mechanical property of fused deposition modelling processed parts","volume":"31","author":"Sood","year":"2010","journal-title":"Mater. Des."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1108\/13552540810862028","article-title":"Effect of processing conditions on the bonding quality of FDM polymer filaments","volume":"14","author":"Sun","year":"2008","journal-title":"Rapid Prototyp. J."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"768","DOI":"10.1016\/j.matdes.2015.06.053","article-title":"Fused deposition modeling with polypropylene","volume":"83","author":"Carneiro","year":"2015","journal-title":"Mater. Des."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Zanjanijam, A.R., Major, I., Lyons, J.G., Lafont, U., and Devine, D.M. (2020). Fused Filament Fabrication of PEEK: A Review of Process-Structure-Property Relationships. Polymers, 12.","DOI":"10.3390\/polym12081665"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Vanaei, H., Shirinbayan, M., Deligant, M., Raissi, K., Fitoussi, J., Khelladi, S., and Tcharkhtchi, A. (2020). Influence of process parameters on thermal and mechanical properties of polylactic acid fabricated by fused filament fabrication. Polym. Eng. Sci., 1\u201310.","DOI":"10.1002\/pen.25419"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1002\/pat.4787","article-title":"Influence of fused deposition modeling parameters on the mechanical properties of ABS parts","volume":"31","author":"Vicente","year":"2020","journal-title":"Polym. Adv. Technol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"771","DOI":"10.1007\/s11664-014-3425-6","article-title":"Thermo-mechanical Characterization of Metal\/Polymer Composite Filaments and Printing Parameter Study for Fused Deposition Modeling in the 3D Printing Process","volume":"44","author":"Hwang","year":"2013","journal-title":"J. Electron. Mater."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Izdebska, J., and Thomas, S. (2016). Printing on Polymers: Theory and Practice. Printing on Polymers: Fundamentals and Applications, William Andrew.","DOI":"10.1016\/B978-0-323-37468-2.00001-4"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Kuznetsov, V.E., Solonin, A.N., Urzhumtsev, O.D., Schilling, R., and Tavitov, A.G. (2018). Strength of PLA Components Fabricated with Fused Deposition Technology Using a Desktop 3D Printer as a Function of Geometrical Parameters of the Process. Polymers, 10.","DOI":"10.20944\/preprints201803.0036.v1"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1016\/j.matdes.2014.02.038","article-title":"Mechanical properties of components fabricated with open-source 3D printers under realistic environmental conditions","volume":"58","author":"Tymrak","year":"2014","journal-title":"Mater. Des."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Waseem, M., Salah, B., Habib, T., Saleem, W., Abas, M., Khan, R., Ghani, U., and Siddiqi, M. (2020). Multi-Response Optimization of Tensile Creep Behavior of PLA 3D Printed Parts Using Categorical Response Surface Methodology. Polymers, 12.","DOI":"10.3390\/polym12122962"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Gosset, A., Barreiro-Villaverde, D., Permuy, J.C., Lema, M., Ares-Pernas, A., and L\u00f3pez, M.J. (2020). Experimental and Numerical Investigation of the Extrusion and Deposition Process of a Poly(lactic Acid) Strand with Fused Deposition Modeling. Polymers, 12.","DOI":"10.3390\/polym12122885"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"618","DOI":"10.1108\/RPJ-09-2013-0093","article-title":"Evaluation of dimensional accuracy and material properties of the makerbot 3D desktop printer","volume":"21","author":"Melenka","year":"2015","journal-title":"Rapid Prototyp. J."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"812","DOI":"10.2507\/28th.daaam.proceedings.114","article-title":"Research of ABS and PLA Materials in the Process of Fused Deposition Modeling Method","volume":"28","author":"Milde","year":"2017","journal-title":"Ann. DAAAM Proc."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"55","DOI":"10.4028\/www.scientific.net\/AMM.465-466.55","article-title":"Evaluation of FDM pattern with ABS and PLA material","volume":"465\/466","author":"Hafsa","year":"2013","journal-title":"Appl. Mech. Mater."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Rodr\u00edguez-Panes, A., Claver, J., and Camacho, A.M. (2018). The influence of Manufacturing Parameters on the Mechanical Behaviour of PLA and ABS Pieces Manufactured by FDM: A comparative Analysis. Materials, 11.","DOI":"10.3390\/ma11081333"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1080\/15459624.2017.1285489","article-title":"Is 3D printing safe? Analysis of the thermal treatment of thermoplastics: ABS, PLA, PET, and nylon","volume":"14","author":"Wojtyla","year":"2017","journal-title":"J. Occup. Environ. Hyg."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"12044","DOI":"10.1021\/acs.est.5b02805","article-title":"Emissions of nanoparticles and gaseous material from 3D printer operation","volume":"49","author":"Kim","year":"2015","journal-title":"Environ. Sci. Technol."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Rubies, E., and Palac\u00edn, J. (2020). Design and FDM\/FFF Implementation of a Compact Omnidirectional Wheel for a Mobile Robot and Assessment of ABS and PLA Printing Materials. Robotics, 9.","DOI":"10.3390\/robotics9020043"},{"key":"ref_26","first-page":"2341","article-title":"Evaluating the Mechanical Properties of Commonly Used 3d Printed ABS and PLA Polymers with Multi-Layered Polymers","volume":"8","author":"Shabana","year":"2019","journal-title":"Int. J. Eng. Adv. Technol."},{"key":"ref_27","unstructured":"Mudassir, A. (2016). Measuring Accuracy of Two 3D Printing Materials, Department of Engineering Technologies, Bowling Green State University."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3213","DOI":"10.1021\/ma010858o","article-title":"Healing of Thermoplastic Polymers at an interface under Nonisothermal Conditions","volume":"35","author":"Yang","year":"2020","journal-title":"Macromolecules"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/j.jmatprotec.2017.02.026","article-title":"Estimation of filament temperature and adhesion development in Fused Deposition Techniques","volume":"245","author":"Costa","year":"2017","journal-title":"J. Mater. Process. Technol."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1721","DOI":"10.1016\/S0014-3057(03)00054-5","article-title":"The enthalpy of fusion and degree of crystallinity of polymers as measured by DSC","volume":"39","author":"Kong","year":"2003","journal-title":"Eur. Polym. J."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"266","DOI":"10.12913\/22998624\/94325","article-title":"Thermovisual measurements of 3D printing of ABS and PLA filaments","volume":"12","author":"Zgryza","year":"2020","journal-title":"Adv. Sci. Technol. Res. J."},{"key":"ref_32","first-page":"1","article-title":"Thermal conditions affecting heat transfer in FDM\/FFE: A contribution towards the numerical modelling of the process","volume":"10","author":"Costa","year":"2014","journal-title":"Virtual Phys. Prototyp."},{"key":"ref_33","unstructured":"Costa, S.F., Duarte, F.M., and Covas, J.A. (2015, January 6\u201310). An Analytical Solution for Heat Transfer during deposition in extrusion-based 3D Printing techniques. Proceedings of the 15th International Conference Computational and Mathematical Methods in Science and Engineering, Rota Cadiz, Spain."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"49747","DOI":"10.1002\/app.49747","article-title":"Experimental study of PLA thermal behavior during fused filament fabrication","volume":"138","author":"Vanaei","year":"2020","journal-title":"J. Appl. Polym. Sci."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Costa, S., Duarte, F., and Covas, J. (2011). Using MATLAB to Compute Heat Transfer in Free Form Extrusion. MATLAB\u2014A Ubiquitous Tool for the Practical Engineer, InTech.","DOI":"10.5772\/23512"},{"key":"ref_36","unstructured":"Holman, J.P. (2010). Heat Transfer, McGraw-Hill Brasil."}],"container-title":["Computers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-431X\/10\/2\/19\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:18:27Z","timestamp":1760159907000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-431X\/10\/2\/19"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,1]]},"references-count":36,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,2]]}},"alternative-id":["computers10020019"],"URL":"https:\/\/doi.org\/10.3390\/computers10020019","relation":{},"ISSN":["2073-431X"],"issn-type":[{"value":"2073-431X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,2,1]]}}}