Cellularization modeling of a rubber compound in injection molding conditions

International audienceThe objective of this work is to develop a numerical model allowing to predict the foaming process of a rubber matrix in injection molding conditions. This is achieved in two parts. The first one is a microscale model that describes the growth of a bubble, based on Amon and Denson’s work [1], according to whom the foam is divided into identical cells consisting in a bubble enveloped by a spherical fluid shell that contains a limited supply of gas generated by a chemical reaction. As the dissolved gas diffuses towards the bubble, the pressure increases, inducing its growth. The model comprises a set of equations describing the evolution of the bubble radius, its pressure, and the concentration gradient inside the shell. Boundary conditions and physical parameters of the rubber-gas system must be found.The rubber undergoes vulcanization during the molding step, so the viscosity increase due to crosslinking was implemented by means of an empirical model. The state of cure evolution was predicted using Kamal-Sourour’s autocatalytic kinetic model [2]. In addition, the coupling of this reaction with the kinetics of the chemical blowing agent’s thermal decomposition is also considered [3].The second part will consist in coupling the microscale model with a macroscale simulation of the injection molding process, including the polymer flow into the cavity during the filling step and the evolution of its temperature throughout the molding stage.The bubble growth kinetics will be described and discussed in view of the gas concentration evolution and the vulcanization kinetics. A parametric study will be conducted to determine first order parameters of the bubble growth process. Predictions of the bubble growth model (bubble size and foam density evolution) will be compared with experimental injection molding data (foam density and bubble size distribution) to validate the model. Acknowledgements.This work was performed within the framework of the chair DEEP, between Hutchinson, ESPCI and MINES Paris - PSL. Hutchinson SA is acknowledged for its financial and technical support. This work is also supported by the French Minister of Research (ANRT).References.1.M. Amon and D. Denson, Polym. Eng. Sci. 24 (1984),10262. M. R. Kamal. Polym. Eng. Sci. 14 (1974), 2313.N. Alcalá et al. Polymers. 14 (2022), 110