Modeling of the dynamic of polymer-glass fibers composites

L. LUDUEÑA; J. GONZALEZ; V. ALVAREZ; JOSE CARELLA; CARLOS DORAO

Praga

Conferencia; 7th International Conference: NANOSTRUCTURED POLYMERS AND NANOCOMPOSITES; 2012

Many high performance products are made based on thermoplastic/fiber composites by means of injection molding processes [1]. Automobile interior and exterior parts are injected with fiber-reinforced thermoplastics to reduce costs, seeking long service life under the automobile hood, exposed to heat, steam and oil [2-4]. For a given polymer/fiber system with fixed reinforcement volume fraction, the performance of the composite material depends mainly on the final fibers aspect ratio and orientation [5]. The shear forces induced in injection molding processes produce fiber breakage which detriments the final properties of the material. Therefore, the prediction of the evolution of the topology of the fibers during the molding process is a critical aspect for obtaining an optimal final product. The fibers in the runners can be characterized as a population of entities that break as they move along the capillary. As such, the population balance equation (PBE) [6] can be used to study the evolution of the fibers. This equation makes a statistical description of the evolution of a group of entities, and has been applied to a large variety of problems in physics, biology, chemistry and engineering, as reviewed by Ramkrishna [6]. To the authors' best knowledge, the PBE has not yet been used to study polymer-glass fiber composites. The PBE uses a density function as its main variable, defined as function of time, physical coordinates, and internal coordinates. The latter are used to represent properties of the entities, such as size, mass, temperature, composition, etc.. For a dispersed phase case, the density function is affected by convection and by the death and birth of entities. In the case of fiber extrusion, the latter are given by breakage events. The resulting equation is integro-differential. Several methods have been proposed to solve this equation, as reviewed by Ramkrishna [6]. The great majority involves re-writing the PBE as a system of differential equations. Recently, Dorao et al. [7] have shown the applicability of the least squares method to solve the PBE directly. Since then, the method and its spectral element version has been successfully applied to study droplets [8] and bubbly flow [9] using the PBE. The aim of this work is to develop a simple model to predict the evolution of the rupture of fibers of polymer-glass fiber composites flowing throughout a capillary at controlled flow fields using the PBE. For this, the least squares spectral method will be used. To our knowledge, this problem was not previously resolved by this methodology.