Structure Development in Injection Molding: A 3D Simulation with a Differential Formulation of the Kinetic Equations

Abstract

A 3D Simulation with a Differential Formulation of the Kinetic EquationsThe purpose of the present work is to introduce a crystallization law into Rem3D, a 3D code written in C++ and dedicated to the injection molding of polymers. We kept the basic hypotheses of Avrami's model and cast the kinetic equations into a differential system that is solved numerically. The variation of the density of potential nuclei with temperature is taken into account. Furthermore, the distribution of mean spherulite sizes can be deduced from the calculations. The second part of the paper is an experimental study of crystallization in well-controlled conditions (2D, isothermal or constant cooling-rate). It establishes a procedure for the determination of the nucleation and growth parameters used in the theoretical model, and gives a first validation of this model. Finally, the crystallization equations are introduced into Rem3D, in order to assess the feasibility of our new approach. Some typical results concerning the evolution of the transformed volume fraction in injection-molded parts are presented.

Experimental study of crystallization of PolyEtherEtherKetone (PEEK) over a large temperature range using a nano-calorimeter

“…A differential form of this approach has been advanced by Patel and Spruiell [13]. An alternative to these models is the use of a system of differential "rate equations" [14][15][16].…”

Model Development and Validation of Crystallization Behavior in Injection Molding Prototype Flows

“…[8][9][10] The growth rate of spherulites was described by the Hoffman-Lauritzen expression. [11] Smirnova et al [12] used a differential set of Avrami equations to predict crystallinity and the average size of spherulites in injection molding, but in their study only temperature effects were taken into account. In a different study, Pantani et al [13] investigated the effect of varying the packing pressure on the morphology of injection molded samples.…”

Identification of crystallization kinetics parameters by genetic algorithm in non‐isothermal conditions

“…Since, we consider an Eulerian context, the position of the interface is treated as a scalar field, that is transported by the velocity field by solving an advection equation. In a previous paper (Smirnova et al , 2005a, b), a volume of fluid technique had been used to determine the flow front position, by transporting the volume fraction of filled polymer on each mesh element.…”

“…Knowing the temperature distribution at a certain instant, we solve crystallization kinetics, through the nonlinear system of equations: Equation 37 where: Equation 38 In the previous paper (Smirnova et al , 2005a, b), we have shown that Rem3D ® numerical resolution of this type of evolution problems was based on the space‐time finite discontinuous Galerkin finite element method. As for the temperature and the free surface, we have chosen to consider here a spatial continuous approximation.…”

“…The material properties for the constitutive equations are detailed in Smirnova et al (2005a, b). It is injected at 220°C, and we consider a simplified boundary condition in temperature (a uniform temperature of 50°C on the surface of the cavity).…”