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The anisotropic elastic properties of injection molded composites are fundamentally coupled to the flow of the fiber suspension during mold-filling. Regarding the modeling of mold-filling processes, both a decoupled and a flow–fiber coupled approach are possible. In the latter, the fiber-induced viscous anisotropy is considered in the computation of the flow field. This in turn influences the evolution of the fiber orientation compared to the decoupled case. This study investigates how flow–fiber coupling in mold-filling simulation affects the stress field in the solid composite under load based on the final elastic properties after fluid–solid transition. Furthermore, the effects of Newtonian and non-Newtonian polymer matrix behavior are investigated and compared. The entire process is modeled micromechanically unified based on mean-field homogenization, both for the fiber suspension and for the solid composite. Different numerical stabilization methods of the mold-filling simulation are discussed in detail. Short glass fibers with a typical aspect ratio of 20 and a volume fraction of 20% are considered, embedded in polypropylene matrix material. The results show that the flow–fiber coupling has a large effect on the fiber orientation tensor in the range of over ± 30% with respect to the decoupled simulation. As a consequence, the flow–fiber coupling affects the stress field in the solid composite under load in the range of over ± 10%. In addition, the predictions based on a non-Newtonian modeling of the matrix fluid differ significantly from the Newtonian setup and thus the necessity to consider the shear-thinning behavior is justified in a quantifiable manner. [ABSTRACT FROM AUTHOR]

Mean-field homogenization is an established and computationally efficient method estimating the effective linear elastic behavior of composites. In view of short-fiber reinforced materials, it is important to homogenize consistently during process simulation. This paper aims to comprehensively reflect and expand the basics of mean-field homogenization of anisotropic linear viscous properties and to show the parallelism to the anisotropic linear elastic properties. In particular, the Hill–Mandel condition, which is generally independent of a specific material behavior, is revisited in the context of boundary conditions for viscous suspensions. This study is limited to isothermal conditions, linear viscous and incompressible fiber suspensions and to linear elastic solid composites, both of which consisting of isotropic phases with phase-wise constant properties. In the context of homogenization of viscous properties, the fibers are considered as rigid bodies. Based on a chosen fiber orientation state, different mean-field models are compared with each other, all of which are formulated with respect to orientation averaging. Within a consistent mean-field modeling for both fluid suspensions and solid composites, all considered methods can be recommended to be applied for fiber volume fractions up to 10%. With respect to larger, industrial-relevant, fiber volume fractions up to 20%, the (two-step) Mori–Tanaka model and the lower Hashin–Shtrikman bound are well suited. [ABSTRACT FROM AUTHOR]

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 ± 5 % in the channel and ± 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. [ABSTRACT FROM AUTHOR]

A novel closure approximation method for fiber orientation tensors is proposed namely the fully symmetric implicit closure. Besides the full index symmetry, implicitly formulated closures based on the contraction condition fulfill the trace condition and the trace-preserving property of the Folgar–Tucker equation. As a first example, the fully symmetric implicit quadratic closure is considered as a simple modification of a recently proposed symmetric quadratic closure. It is shown that this closure can be realized by a fiber orientation distribution function. Secondly, the fully symmetric implicit hybrid closure is proposed as a counter-example of a closure not being based on a orientation distribution function. Both closures are compared against classical approximations in view of orientation evolution in a simple shear flow. Furthermore, the capability of predicting the effective viscous and elastic behavior of fiber suspensions and solid composites is investigated for a given fiber orientation state. The results show that the proposed implicit closures can be used to approximate the maximum entropy closure. Thereby, both the quadratic and the hybrid approach alleviate the high computational burden of the maximum entropy closure, as their evaluation requires solving a one-dimensional problem only. In addition, the predicted effective behavior based on the implicit closures shows an overall good agreement with predictions based on measured orientation data. • A novel implicit closure approach for fiber orientation tensors is proposed. • By considering full index symmetry, all necessary algebraic properties are fulfilled. • The considered closures can be reduced to an efficiently solvable 1D formulation. • The closures show a reliable prediction of effective viscous and elastic properties. • The closures considered are efficient maximum entropy approximations. [ABSTRACT FROM AUTHOR]