Constitutive modeling of the rheological behavior of platelet suspensions
Compression molding of chopped fiber composites is used to manufacture complex 3D geometries with high fiber volume fractions of 50-60% and long, discontinuous fibers and thermoplastic matrices. When prepreg, chopped into platelets, is used as a charge material, the individual platelets remain intact during the molding process and flow relative to one another, as experimental observations show. Heterogeneity of the platelet/resin suspension cannot be considered at the structural scale of molding simulation. Instead, the suspension should be idealized into the homogenized anisotropic and viscous system which obeys the prescribed anisotropic stress-strain rate constitutive relation. The viscosity tensor of the aforementioned constitutive law was analytically evaluated in this work through the representative volume element (RVE) based analysis. An idealized microstructure of platelets was developed to perform such an analysis. The platelets were aligned and arranged in a planar configuration with periodic boundary conditions. Analytic expressions for the effective, anisotropic viscosities were derived by micromechanical analysis for the idealized microstructure of rigid platelets. In this analysis, the load transfer mechanisms and their contribution to the viscosity of the platelet assembly were investigated. The kinematic assumption of linear velocity distributions consistent with the mechanism of shearing rate was adopted. While the platelets were assumed to be rigid, the resin was taken as an incompressible, isotropic fluid which provided for the platelet-to-platelet load transfer. Strain rate and temperature dependence were included by modeling the polymer matrix as a Carreau fluid. Shear strain in the resin was developed due to the relative motion of adjacent platelets. The resin shear strain rate was expressed in terms of the corresponding platelet velocities. Equilibrium of the platelet was used to relate the applied far-field stress to the average strain rate through the viscosity of neat resin and geometric parameters of the RVE constituents. When combined, these parameters defined the effective homogenized viscosities of an anisotropic system equivalent to the platelet/resin suspension. The expressions for the effective viscosities were found to be dependent on the platelet geometry, stack geometry, the platelet volume fraction and the viscosity of neat resin. In this study, the platelet volume fraction was defined as the volume of platelets within the RVE divided by the RVE volume and discriminated from the fiber volume fraction within a platelet. An approach using the "viscous solid analogy'' was developed to leverage structural finite element methods to predict homogenized viscosities of the platelet assembly. A finite element model was constructed to develop a comparison to the analytic expressions for rigid platelets and include the effect of deformation within the platelets. To compare with the analytic expressions, large viscosities were prescribed for the platelet to approximate rigidity. The properties of the deformable platelets were determined by an approach proposed by Pipes and co-workers. The assumption of rigidity was found to be approximate except in the case of elongation along the fiber direction. A laminate analogy was implemented as a homogenization tool to include the effect of orientation on the apparent viscosities of a multi-axial platelet assembly. The aligned platelet suspension was used to predict the `pseudo-ply' properties. Pseudo-laminates, which were assumed to approximate the microstructure, were developed. The effective `pseudo-laminate' viscosities were predicted with classical lamination theory.
Pipes, Purdue University.
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