Coupled simulation of flow-induced viscous and elastic anisotropy of short-fiber reinforced composites

Abstract

The present work discusses the impact of the back coupling of the fiber orientation distribution on the base flow and on the fiber orientation itself during mold filling simulations. Flows through a channel and over a backward-facing step are investigated. Different closure approximations are considered for modeling the flow-induced evolution of anisotropy. The results corresponding to the decoupled approach, in which the effect of fibers on local fluid properties is neglected, build the basis of comparison. The modeling is limited to a laminar, incompressible, and isothermal flow of a fiber suspension consisting of rigid short fibers suspended in an isotropic Newtonian matrix fluid. A linear, anisotropic constitutive law is used in combination with a uniform fiber volume fraction of 10% and an aspect ratio of 10. To evaluate the impact of back coupling and of different closure methods in view of the manufactured solid composite the resulting anisotropic elastic properties are investigated based on the Mori–Tanaka method combined with an orientation average scheme. Relative to the range [0, 1] the pointwise difference in fiber orientation between the decoupled and the coupled approach is found to be $$\pm 5{\%}$$ ± 5 % in the channel and $$\pm 30{\%}$$ ± 30 % in the backward-facing step, respectively. The viscosity and the elasticity tensor show both significant flow-induced anisotropies as well as a strong dependence on closure and coupling.

Unified mean-field modeling of viscous short-fiber suspensions and solid short-fiber reinforced composites

“…In view of flow-fiber coupled generation of fiber orientation data based on fiber-induced anisotropic viscous behavior [3,[6][7][8][9], a uniform mean-field modeling can be applied based on the present work. In case of viscous fiber suspensions, the presented mean-field models can be applied to replace well-known fiber suspension models from the literature, e.g., [79,86,87].…”

“…These components are manufactured by injection molding of fiber suspensions consisting of liquid polymer matrix and suspended fibers. During processing, the local kinematic conditions within the flow influence the evolution of the fiber orientation state which in turn influences the anisotropic elastic properties after the fluid-solid transition of the polymer matrix [3,4]. In view of flow-fiber coupling, the orientation state itself induces anisotropic viscous behavior that affects the flow, which in turn affects the evolution of fiber orientation [3,[5][6][7][8][9].…”

“…During processing, the local kinematic conditions within the flow influence the evolution of the fiber orientation state which in turn influences the anisotropic elastic properties after the fluid-solid transition of the polymer matrix [3,4]. In view of flow-fiber coupling, the orientation state itself induces anisotropic viscous behavior that affects the flow, which in turn affects the evolution of fiber orientation [3,[5][6][7][8][9]. As a consequence, a physically comprehensive simulation is required to consider the anisotropic viscosity already during mold filling to better represent both the flow kinematics and the evolution of the orientation state [4,10].…”

“…By [3]. Since ε and D are symmetric, C = C T R and V = V T R is usually introduced for convenience but is not required in general.…”

“…Furthermore, tr( D) = 0 is valid only numerically in incompressible fluid solvers and in this context P 2 VP 2 forces to map only the deviatoric part of D. In addition, the viscous stress is forced to be deviatoric. The issue of non-deviatoric viscous stress in the context of defining a pressure is addressed in Karl et al [3] and in Ponte Castañeda [95].…”