Modeling Compression Flow for In-Plane Isotropic Laminated Materials Using Anisotropy-Based Effective Shear Viscosity

This paper aims to establish a theoretical framework linking the macroscopic in-plane isotropic laminated structure of fiber-reinforced resin materials, such as sheet molding compounds (SMC) and randomly oriented strand (ROS) composites, to their flow behavior. These materials exhibit plug flow-like behavior during compression molding. However, conventional models for SMC’s flow behavior have inherent limitations, necessitating improvements by thoroughly examining the relationship between the laminated structure and flow modes. In this work, we introduce a decomposition of the strain rate tensor and derive an anisotropic stress tensor tailored to the material’s symmetry and anisotropy. Furthermore, we propose an effective shear viscosity model that integrates the anisotropic stress induced by the laminated structure into general-purpose computational fluid dynamics (CFD) software. To assess the characteristics of the proposed viscosity model, we conduct numerical simulations of the compression molding process, systematically varying the ratio of out-of-plane compression viscosity to out-of-plane shear viscosity. Without arbitrary modifications to the wall boundary conditions, simulations with a high viscosity ratio successfully predict the formation of layers with variable viscosities and velocity distributions indicative of plug flow-like behavior. This behavior is attributed to the out-of-plane shear flow region adjacent to the walls, acting as a low-viscosity lubricating layer.