The numerical prediction of crystallization transformation is of great interest in several applications. One such application is the polymer-forming process. In this short communication, the integration of the widely used Nakamura kinetics is discussed. A robust time integration method is proposed. In order to overcome its singularities, the Nakamura function is thresholded. A convergence analysis provides guidelines for the threshold values and time discretization.
| Published in | International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 4) |
| DOI | 10.11648/j.ijtam.20170304.13 |
| Page(s) | 143-147 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2017. Published by Science Publishing Group |
Crystallization Kinetics, Nakamura, Time Integration, Robust, Phase Change
| [1] | ANSYS Inc. Polyflow technical specifications. Technical Report 2007. |
| [2] | Autodesk. Moldflow Users manual 2016. |
| [3] | Moldex 3D. Users Manual 2016. |
| [4] | Baran I, Cinar K, Ersoy N, Akkerman R, Hattel JH. A Review on the Mechanical Modeling of Composite Manufacturing Processes. Archives of Computational Methods in Engineering 2016;. |
| [5] | Patel RM, Spruiell JE. Crystallization Kinetics During Polymer Processing -Analysis of Available Approaches for Process Modeling. Polymer Engineering and Science 1991; 31 (10): 730–738. |
| [6] | Faraj J, Pignon B, Bailleul JL, Boyard N, Delaunay D, Orange G. Heat Transfer and Crystallization Modeling during Compression Molding of Thermoplastic Composite Parts. Key Engineering Materials 2015; 651-653: 1507–1512. |
| [7] | Cogswell FN. Thermoplastic aromatic polymer composites. Woodhead: Cambridge UK., 1992. |
| [8] | Boyard N. Heat Transfer in Polymer Composite Materials: Forming Processes. John Wiley & Sons: Hoboken NJ, 2016. |
| [9] | Avrami M. Kinetics of phase change. I General theory. The Journal of Chemical Physics 1939; 7: 1103. |
| [10] | Haudin JM, Monasse B. Physico-chimie des polymères. Initiation à la chimie et à la physico-chimie macromoléculaires. chap. VII, Groupe Fran, 1996. |
| [11] | Nakamura K, Katayama K, Amano T. Some aspects of nonisothermal crystallization of polymers. II. Consideration of the isokinetic condition. Journal of Applied Polymer Science 1973; 17 (4): 1031–1041. |
| [12] | Billon N, Barq P, Haudin JM. Modelling of the Cooling of Semi-crystalline Polymers during their Processing. International Polymer Processing 1991; 6 (4): 348–355. |
| [13] | Patel RM. Crystallization Kinetics Modeling of High Density and Linear Low Density Polyethylene Resins. Journal of Applied Polymer Science 2012; 124: 1542–1552. |
| [14] | Tardif X, Pignon B, Boyard N, Schmelzer JW, Sobotka V, Delaunay D, Schick C. Experimental study of crystallization of PolyEtherEtherKetone (PEEK) over a large temperature range using a nano-calorimeter. Polymer Testing 2014; 36: 10–19. |
| [15] | Neugebauer F, Ploshikhin V, Ambrosy J, Witt G. Isothermal and non-isothermal crystallization kinetics of polyamide 12 used in laser sintering. Journal of Thermal Analysis and Calorimetry 2016; 124 (2): 1–9. |
| [16] | Levy A, Le Corre S, Sobotka V. Heat transfer and crystallization kinetics in thermoplastic composite processing. A coupled modelling framework. ESAFORM 19, Nantes, France, 2016. |
| [17] | Pignon B, Tardif X, Lefèvre N, Sobotka V, Boyard N, Delaunay D. A new PvT device for high performance thermoplastics: Heat transfer analysis and crystallization kinetics identification. Polymer Testing 2015; 45: 152–160. |
| [18] | Somé SC, Delaunay D, Faraj J, Bailleul JL, Boyard N, Quilliet S. Modeling of the thermal contact resistance time evolution at polymer-mold interface during injection molding: Effect of polymers’ solidification. Applied Thermal Engineering 2015; 84: 150–157. |
| [19] | Amado A, Wegener K, Schmid M, Levy G. Characterization and modeling of non-isothermal crystallization of Polyamide 12 and co-Polypropylene during the SLS process. 5th International Polymers and Moulds Innovations Conference, Ghent, Belgium, 2012; 207–216. |
| [20] | Joshi SC, Lam YC. Integrated approach for modelling cure and crystallization kinetics of different polymers in 3D pultrusion simulation. Journal of Materials Processing Technology 2006; 174 (1-3): 178–182. |
| [21] | Le Goff R, Poutot G, Delaunay D, Fulchiron R, Koscher E. Study and modeling of heat transfer during the solidification of semi-crystalline polymers. International Journal of Heat and Mass Transfer 2005; 48 (25-26): 5417–5430. |
| [22] | Chan T, Isayev A. Quiescent polymer crystallization: Modeling and measurements. Polymer Engineering and Science 1994; 34 (6): 461–471. |
| [23] | Kenny JM, Maffezzoli A, Nicolais R. A new kinetic model for polymer crystallization by calorimetric analysis. Thermochimica Acta 1993; 227 (December 1992): 83–95. |
| [24] | Bessard E, De Almeida O, Bernhart G. Unified isothermal and non-isothermal modelling of neat PEEK crystallization. Journal of Thermal Analysis and Calorimetry 2014; 115 (2): 1669–1678. |
| [25] | Velisaris CN, Seferis JC. Crystallization Kinetics of Polyetheretherketone (PEEK). Polymer Engineering and Science 1986; 26 (22): 1574. |
APA Style
Arthur Levy. (2017). Robust Numerical Resolution of Nakamura Crystallization Kinetics. International Journal of Theoretical and Applied Mathematics, 3(4), 143-147. https://doi.org/10.11648/j.ijtam.20170304.13
ACS Style
Arthur Levy. Robust Numerical Resolution of Nakamura Crystallization Kinetics. Int. J. Theor. Appl. Math. 2017, 3(4), 143-147. doi: 10.11648/j.ijtam.20170304.13
AMA Style
Arthur Levy. Robust Numerical Resolution of Nakamura Crystallization Kinetics. Int J Theor Appl Math. 2017;3(4):143-147. doi: 10.11648/j.ijtam.20170304.13
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Download@article{10.11648/j.ijtam.20170304.13,
author = {Arthur Levy},
title = {Robust Numerical Resolution of Nakamura Crystallization Kinetics},
journal = {International Journal of Theoretical and Applied Mathematics},
volume = {3},
number = {4},
pages = {143-147},
doi = {10.11648/j.ijtam.20170304.13},
url = {https://doi.org/10.11648/j.ijtam.20170304.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20170304.13},
abstract = {The numerical prediction of crystallization transformation is of great interest in several applications. One such application is the polymer-forming process. In this short communication, the integration of the widely used Nakamura kinetics is discussed. A robust time integration method is proposed. In order to overcome its singularities, the Nakamura function is thresholded. A convergence analysis provides guidelines for the threshold values and time discretization.},
year = {2017}
}
TY - JOUR T1 - Robust Numerical Resolution of Nakamura Crystallization Kinetics AU - Arthur Levy Y1 - 2017/10/23 PY - 2017 N1 - https://doi.org/10.11648/j.ijtam.20170304.13 DO - 10.11648/j.ijtam.20170304.13 T2 - International Journal of Theoretical and Applied Mathematics JF - International Journal of Theoretical and Applied Mathematics JO - International Journal of Theoretical and Applied Mathematics SP - 143 EP - 147 PB - Science Publishing Group SN - 2575-5080 UR - https://doi.org/10.11648/j.ijtam.20170304.13 AB - The numerical prediction of crystallization transformation is of great interest in several applications. One such application is the polymer-forming process. In this short communication, the integration of the widely used Nakamura kinetics is discussed. A robust time integration method is proposed. In order to overcome its singularities, the Nakamura function is thresholded. A convergence analysis provides guidelines for the threshold values and time discretization. VL - 3 IS - 4 ER -
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