A numerical approach to design dual-scale porosity composite reinforcements with enhanced permeability

Highlights: • Principles for the design of multi-scale material with enhanced permeability are proposed. • A scale separation criterion for in-plane flow through multi-scale structure is established. • Effects of micro- and meso-scale architecture on macro-permeability are estimated. • Differences in key geometrical parameters affecting in-plane and through-thickness flow are highlighted. • Design of quasi-unidirectional non-crimp fabrics using established rules is presented. Fibrous composite reinforcements with enhanced permeability are of a particular interest for liquid composite molding processes requiring the fibrous preforms to be well impregnated by a viscous polymer. The aim of this work is to study the link between the reinforcement permeability and the geometrical parameters of its architecture, taking into account the internal multi-scale porosity distribution by employing the Brinkman equation. In order to design a reinforcement with the enhanced permeability without degrading mechanical properties of a final composite part, the study is conducted with the condition of fixed and high fiber volume fraction. The Proper Generalized Decomposition method, due to its principle of separation of variables, allowed to efficiently compute the solution of the problem for a range of geometrical parameters at once, as opposed to the classical parametric study. A scale separation criterion for in-plane flow was proposed. It estimates when the microscopic intra-yarn flow can be neglected compared to the mesoscopic inter-yarn flow. The major contributing parameters to the enhancement of both the in-plane and through-thickness permeabilities were identified. Principles established in this study were applied to the design of quasi-unidirectional non-crimp fabrics, where the permeability enhancement was evidenced.