A new PvT device for high performance thermoplastics: Heat transfer analysis and crystallization kinetics identification

Pignon, Baptiste; Tardif, Xavier; Lefèvre, Nicolas; Sobotka, Vincent; Boyard, Nicolas; Delaunay, Didier

doi:10.1016/j.polymertesting.2015.05.013

Cited by 29 publications

(24 citation statements)

References 31 publications

(36 reference statements)

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“…Thus, equation (2) should be integrated in a global multiphysical integration scheme. For such applications, the reader may refer to references [16,17,19,20,21,22].…”

Section: Resultsmentioning

confidence: 99%

“…The Nakamura function G is plotted over [0,1] in Figure 1. This differential form, a first-order non-linear ordinary differential equation, is more natural to implement and solve numerically, especially in a multiphysical framework [16,17,18,19,20,21,22,23]. The initial state of the material (amorphous or semi-crystalline) should be given as an initial condition for α.…”

Section: Differential Formmentioning

confidence: 99%

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Robust Numerical Resolution of Nakamura Crystallization Kinetics

Lévy¹

2017

IJTAM

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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.

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“…Thus, equation (2) should be integrated in a global multiphysical integration scheme. For such applications, the reader may refer to references [16,17,19,20,21,22].…”

Section: Resultsmentioning

confidence: 99%

Section: Differential Formmentioning

confidence: 99%

Robust Numerical Resolution of Nakamura Crystallization Kinetics

Lévy¹

2017

IJTAM

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“…However, many published articles [45,46] have shown a nonlinear relationship between the transition temperature and the pressure. Therefore, we used a quadratic polynomial Equation in order to have a more accurate model:…”

Section: Continuous Two-domain Eosmentioning

confidence: 99%

“…The material-dependent constants A, B, and C differ for the two domains. Therefore, the following sets of equations can be used for specific cases: when > ( ), However, many published articles [45,46] have shown a nonlinear relationship between the transition temperature and the pressure. Therefore, we used a quadratic polynomial Equation in order to have a more accurate model:…”

Section: Continuous Two-domain Eosmentioning

confidence: 99%

“…It should be noted that the maximum cooling rate in injection molding can be as high as 3000 • C/min [41]. Several laboratories have reported that they can realize equally high cooling rates [36,41,45], but no commercial pvT instrument is available with such abilities. This further indicates the necessity of predictive models to extrapolate pvT data for higher cooling rates.…”

Section: Influence Of the Ccooling Ratementioning

confidence: 99%

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Continuous Two-Domain Equations of State for the Description of the Pressure-Specific Volume-Temperature Behavior of Polymers

et al. 2020

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The two-domain Schmidt equation of state (EoS), which describes the pressure-specific volume-temperature (pvT) behavior of polymers in both the equilibrium molten/liquid state and non-equilibrium solid/glassy state, is often used in the simulation of polymer processing. However, this empirical model has a discontinuity problem and low fitting accuracy. This work derived a continuous two-domain pvT model with higher fitting accuracy compared with the Schmidt model. The cooling rate as an obvious influencing factor on the pvT behavior of polymers was also considered in the model. The interaction parameters of the equations were fitted with the experimental pvT data of an amorphous polymer, acrylonitrile-butadiene-styrene (ABS), and a semi-crystalline polymer, polypropylene (PP). The fitted results by the continuous two-domain EoS were in good agreement with the experimental data. The average absolute percentage deviations were 0.1% and 0.16% for the amorphous and semi-crystalline polymers, respectively. As a result, the present work provided a simple and useful model for the prediction of the specific volume of polymers as a function of temperature, pressure, and cooling rate.Polymers 2020, 12, 409 2 of 18 rate, and therefore is difficult to model by an analytical approach [21]. The semi-empirical model of Hartmann-Haque (HH) [23,24], on the other hand, showed satisfactory results for amorphous polymers but difficulties for semi-crystalline polymers [21]. Additionally, the specific volume is not a dependent variable in these theoretical and semi-empirical models, leading to difficulties in simulation or prediction. In comparison, empirical models are often convenient to represent pvT data on polymers in analytical form, by only giving the parameters in the correspondent equations [25]. Empirical pvT models include the Spencer-Gilmore model [26], the Schmidt model [27,28], and the Tait model [29,30], which are used in commercial software, e.g., by Moldflow (Autodesk, Inc.), Moldex 3D (CoreTech System Co., Ltd.), Sigmasoft (SIGMA Engineering GmbH) and Cadmould (Simcon kunststofftechnische Software GmbH). The Spencer-Gilmore model is quite simple but less accurate. The Tait model has been widely used for polymers [21,22,31,32], because of its simple form, convenient application, and high precision. The two-domain Tait EoS has much more fitting accuracy, especially in the solid state. The Schmidt model was developed by T.W. Schmidt at the Institute for Plastics Processing (IKV) in 1986 [28]. The two-domain Schmidt EoS is similar to the two-domain Tait EoS, although simpler, and it is primarily used in German-speaking countries [7,8,10]. The Tait model uses a volume-pressure relationship, while the Schmidt model considers a volume-temperature relationship. The Schmidt model has less accuracy than the Tait model [33], and fitting problems occur regularly. Furthermore, another important problem for the two-domain Tait EoS and the Schmidt EoS is the discontinuity of the models. Because the EoS describes the pvT behavior of...

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Experimental Determination and Modeling of Thermophysical Properties

and¹,

Delaunay²

2016

Heat Transfer in Polymer Composite Materials

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A new PvT device for high performance thermoplastics: Heat transfer analysis and crystallization kinetics identification

Cited by 29 publications

References 31 publications

Robust Numerical Resolution of Nakamura Crystallization Kinetics

Robust Numerical Resolution of Nakamura Crystallization Kinetics

Continuous Two-Domain Equations of State for the Description of the Pressure-Specific Volume-Temperature Behavior of Polymers

Experimental Determination and Modeling of Thermophysical Properties

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