A Model for the Flow of a Chopped Fiber Reinforced Polymer Compound in Compression Molding

The flow of a chopped fiber reinforced polymer compound in compression molding is modelled as a two-dimensional membrane-like sheet which extends uniformly through the cavity thickness with slip at the mold surface. The model is consistent with both the kinematic mechanisms observed in actual flow and the three-dimensional anisotropy caused by the arrangement of fibers in the sheet. The material resistance to extension is expressed in a constitutive equation for the two-dimensional stress resultant formed by integrating the planar stress components through the thickness of the cavity. This stress resultant is assumed to be a linear function of the corresponding planar rate of deformation in the molding compound. Through a mechanism of fiber-resin interaction, the material resistance to extension can be characterized by a single scalar function of the transverse temperature distribution. Three alternatives are considered for the friction response at the cavity surface: (i) constant magnitude, (ii) proportional to the relative velocity (hydrodynamic), and (iii) proportional to the normal component of the stress vector (Coulomb). These three assumptions are compared by considering their general implications on the flow-front progression. The latter two are examined in some detail for thin charges in which the material resistance to extension is negligible compared to the effect of friction. Analytical solutions for an elliptical charge are obtained for both hydrodynamic and Coulomb friction. By comparing these solutions with experimental results, we conclude that the hydrodynamic model for the friction response is the best of the three proposed alternatives.